A through-hole-free structure metal environment RFID tag antenna integrated system

Abstract

The application discloses a metal environment RFID tag antenna integrated system without a through-hole structure and relates to the technical field of ultra-high frequency RFID tag antennas. The technical scheme points of the metal environment RFID tag antenna integrated system without a through-hole structure include a flexible base material, a metal conductor pattern, a dielectric layer and an RFID chip. The metal conductor pattern comprises a circular radiation patch in the middle, ground sheets on both sides and short stubs connecting the circular radiation patch and the ground sheets in an unfolded state. The circular radiation patch comprises complementary radiation patches, a complementary sawtooth gap is formed between the two radiation patches, and the RFID chip is connected across the feed ends of the two radiation patches. The short stubs provide a return path for the circular radiation patch to the ground sheet, and the antenna does not contain a metalized through-hole. The effect is that the antenna is convenient for later debugging and error compensation.

Description

Technical Field

[0001] This invention relates to the field of ultra-high frequency radio frequency identification tag antenna technology, and more specifically, to an integrated system of metal environmental RFID tag antennas without through holes. Background Technology

[0002] Passive UHF RFID systems use electromagnetic waves emitted by the reader to power the tag chip and complete information exchange through backscattering. When traditional dipole tags are directly attached to a metal surface, the mirror current generated on the metal surface has a similar amplitude but opposite direction to the current on the radiating patch. This easily causes radiation cancellation, drastic changes in input impedance, and operating frequency shift, resulting in a significant decrease in radiation efficiency and reading distance. Therefore, tag antennas designed for metallic environments not only need to isolate the electromagnetic influence of the metal but also need to achieve conjugate matching between the antenna and the highly capacitive chip within a limited volume.

[0003] Existing solutions mainly include artificial magnetic conductors (AMC) or electromagnetic bandgap (EBG) backplanes, high dielectric constant substrates, planar inverted-F antennas (PIFA), and folded patch structures. While AMC / EBG structures can suppress the influence of metals and improve gain, they typically contain periodic units, are large in size and have many layers, require vias, and have high processing costs. High dielectric constant materials can achieve miniaturization, but material costs and loss control requirements are high. PIFA often relies on metallized vias or short-circuit walls, and resonance is sensitive to the location of vias and short circuits, making debugging and assembly complex.

[0004] While compact foldable surface mount labels have been developed to avoid some metallized vias, they still suffer from issues such as low power transfer coefficient, limited read distance, and sensitivity to soldering and folding tolerances due to chip placement on narrow sidewall leads. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a metal environmental RFID tag antenna integration system without through-hole structure.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A metal environmental RFID tag antenna integration system without through holes includes a flexible substrate, wherein the flexible substrate is provided with a metal conductor pattern, a dielectric layer and a radio frequency identification chip;

[0008] The metal conductor pattern, in its unfolded state, includes a circular radiating patch in the center, grounding plates on both sides, and a short stub connecting the circular radiating patch and the grounding plates.

[0009] The circular radiating patch includes complementary radiating patches with complementary sawtooth gaps between them, and the radio frequency identification chip is connected between the feed terminals of the two radiating patches.

[0010] One of the radiating patches has a U-shaped slit located near the chip;

[0011] The flexible substrate is folded along the short stubs on both sides and then wrapped around the surface of the dielectric layer, so that the circular radiating patch is located on one side of the dielectric layer and the two grounding patches are located on the other side of the dielectric layer, forming a folded patch tag antenna suitable for mounting on a metal surface.

[0012] The stub provides a return path to the grounding plate for the circular radiating patch, and the antenna does not contain metallized vias.

[0013] Preferably, the flexible substrate is a flexible polyimide substrate;

[0014] The metal conductor pattern is formed by shaping and folding a flexible polyimide copper-clad layer.

[0015] Preferably, the dielectric layer is a foam dielectric layer, used to maintain the circular shape of the label and determine the spacing between the circular radiating patch and the grounding plate.

[0016] Preferably, the patch tag antenna is cylindrical with a diameter of 32mm and a thickness of 3mm.

[0017] Preferably, the complementary sawtooth gap is formed by the folded edges of two interlocking radial patches, which is used to extend the surface current path in the feeding area and introduce equivalent inductance to adjust the resonant frequency.

[0018] Preferably, the U-shaped gap is disposed in the region of one of the radiating patches close to the chip to extend the local surface current path and introduce additional inductance to adjust the resonant frequency and input reactance.

[0019] Preferably, the stub connects the circular radial patch to the folded grounding plate respectively. Reducing the width of the stub will enhance the current concentration at that point, thereby increasing the equivalent resistance and equivalent inductance.

[0020] Preferably, the input impedance of the antenna at 0.915 GHz is 3.96 + j191 Ω.

[0021] Preferably, the tag antenna also includes an equivalent circuit model, which equates the complementary radiating patch to a parallel resonant branch, the stub to a series resistor and a series inductor, and the complementary sawtooth slot to a slot capacitor connected across the input terminal. The input impedance is expressed as:

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] in, The input impedance of the tag antenna; and These are the equivalent impedances of the two complementary radiating patches, respectively. This is the total series impedance of the two short stubs; The equivalent capacitive reactance for complementary sawtooth gaps; , This represents the radiation and loss resistance of the two radiating patches. , This represents the corresponding equivalent inductance. , This represents the equivalent capacitance between the radiating patch and the grounding plate. and These represent the total resistance and total inductance of the two short-circuited wires, respectively. This represents the equivalent capacitance of the sawtooth slit. It represents angular frequency.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] The antenna of this invention, after folding, has a tag diameter of 32mm and a thickness of 3mm, with an electrical dimension of approximately 0.0916λ and an overall volume of approximately 2412mm³, allowing it to be mounted on the surface of small metal objects. Furthermore, it achieves highly efficient complex impedance matching by utilizing complementary sawtooth gaps, U-shaped gaps, and double short-circuit stubs to construct a hierarchical inductive tuning structure. At a frequency of 915MHz, the maximum power transfer coefficient is approximately 0.81, effectively driving a high-capacitive chip with an impedance of 10−j191 Ω. Under 4WEIRP testing conditions, the maximum reading distance is 14.3m when the tag is placed on a 200mm×200mm aluminum plate, 13.56m when placed on a 100mm×100mm aluminum plate, and 8.4m in free space. It possesses excellent adaptability to metal platforms. When the tag is installed on the surface of metal containers of different materials, sizes, and shapes, it maintains a reading distance of at least 8 meters within the 905-925MHz operating frequency band. When installed on the surface of a cylindrical aluminum can, the maximum reading distance is approximately 11.35m. The manufacturing process is simple and convenient. The antenna is formed by folding a single flexible polyimide copper-clad layer, eliminating the need for metallized vias, short-circuit walls, lumped tuning elements, or AMC / EBG periodic structures. This effectively reduces production steps and mitigates the adverse effects of assembly errors. It facilitates later debugging and error compensation. The serrated gap parameters handle coarse impedance tuning, while the U-shaped gap parameters handle fine impedance tuning. The tuning effects of each structural parameter are clearly defined, effectively compensating for and correcting operating frequency shifts caused by chip impedance dispersion, folding warpage, and etching errors. Attached Figure Description

[0030] Figure 1 This is a flowchart illustrating an embodiment of the present invention;

[0031] Figure 2 The equivalent circuit elements and complete equivalent circuit of the embodiments of the present invention;

[0032] Figure 3 The results are the reading distance test results of an embodiment of the present invention. Detailed Implementation

[0033] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0034] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0035] Secondly, the term "an embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single embodiment or an embodiment selectively excluded from other embodiments.

[0036] Reference Figures 1-3 As shown.

[0037] The embodiments further illustrate the through-hole-free metal environmental RFID tag antenna integration system proposed in this invention.

[0038] A metal environmental RFID tag antenna integration system without through holes includes a flexible substrate, which is provided with a metal conductor pattern, a dielectric layer and a radio frequency identification chip.

[0039] The unfolded metal conductor pattern includes a circular radiating patch in the center, grounding plates on both sides, and short stubs connecting the circular radiating patch and the grounding plates.

[0040] The circular radiating patch includes complementary radiating patches with complementary sawtooth gaps between them, and the radio frequency identification chip is connected between the feed terminals of the two radiating patches.

[0041] One of the radiating patches has a U-shaped slit located near the chip;

[0042] The flexible substrate is folded along the short lines on both sides and then wrapped around the surface of the dielectric layer, so that the circular radiating patch is located on one side of the dielectric layer and the two grounding patches are located on the other side of the dielectric layer, forming a folded patch tag antenna suitable for mounting on a metal surface.

[0043] The stub provides a return path to the ground plane for the circular radiating patch, and the antenna does not contain metallized vias.

[0044] The flexible substrate is a flexible polyimide substrate;

[0045] The metal conductor pattern is formed by shaping and folding a flexible polyimide copper-clad layer.

[0046] The flexible polyimide substrate serves as the carrier substrate for the antenna structure. The copper-clad layer attached to it is etched and shaped to obtain a metal conductor pattern with a preset unfolded shape. Relying on the flexibility of the polyimide substrate itself, the metal conductor pattern can be bent along the preset stub position. After folding, the circular radiating patch and the two grounding patches separated by the metal conductor pattern are respectively located on two opposite sides of the foam dielectric layer. The foam dielectric layer separates the radiating patch and the grounding patch, thereby fixing the vertical distance between them.

[0047] After folding, the copper-clad conductor pattern establishes an electrical connection loop from the radiating patch to the grounding plate via short stubs on the side of the dielectric layer. This eliminates the need for additional metallized vias penetrating the flexible substrate and dielectric layer to achieve grounding return. The flexible deformation capability of the polyimide substrate ensures that the copper layer does not crack or the conductor pattern detaches during the folding process, thus guaranteeing the integrity of the antenna's electrical path after folding. This ultimately completes the structural forming of the via-less foldable RFID tag antenna.

[0048] The dielectric layer is a foam dielectric layer, used to maintain the circular shape of the label and determine the spacing between the circular radiating patch and the grounding plate.

[0049] The foam dielectric layer serves as the built-in support carrier for the folded tag antenna. After the flexible substrate is bent and wrapped along the stub, the foam dielectric layer is sandwiched between the circular radiating patch and the grounding patch. The thickness of the foam dielectric layer limits the vertical distance between the circular radiating patch and the grounding patch. The equivalent capacitance formed between the radiating patch and the grounding patch is determined by this spacing parameter, thereby regulating the overall resonance characteristics of the antenna.

[0050] The patch tag antenna is cylindrical, with a diameter of 32mm and a thickness of 3mm.

[0051] The diameter limits the lateral coverage of the circular radiating patch and determines the maximum extension length of the current on the surface of the radiating patch, thereby constraining the basic range of the antenna's resonant frequency. The thickness corresponds to the thickness of the foam dielectric layer, which is the vertical distance between the circular radiating patch and the ground plate. The size of this distance can change the value of the equivalent capacitance generated between the radiating patch and the ground plate, thereby adjusting the overall input impedance parameters of the antenna.

[0052] The complementary sawtooth gap is formed by the folded edges of two interlocking radial patches, which is used to extend the surface current path in the feeding area and introduce equivalent inductance to adjust the resonant frequency.

[0053] When an RF signal is input to the feed area, the conduction current generated on the surface of the radiating patch flows along the serrated folded edges. The serrated folded structure extends the actual path of the surface current within the feed area. This extended current path introduces an equivalent inductance into the feed circuit, changing the overall inductance parameters of the antenna. This adjusts the antenna's resonance conditions, ultimately controlling the antenna's resonant frequency.

[0054] The U-shaped slot is placed in the region of one of the radiating patches close to the chip to extend the local surface current path and introduce additional inductance to adjust the resonant frequency and input reactance.

[0055] When the radio frequency signal is conducted to this area, the local current flowing on the surface of the radiating patch will travel along the curved contour of the U-shaped gap, thereby extending the actual flow path of the local surface current at this location. After the current path is extended, an additional inductance is introduced into the antenna circuit. After the inductance parameters change, the resonant frequency and input reactance parameters of the antenna can be adjusted, thereby achieving optimized matching of the antenna's electrical performance.

[0056] The short stubs connect the circular radial patch to the folded grounding plate respectively. Reducing the width of the short stubs will increase the current concentration at that point, thereby increasing the equivalent resistance and equivalent inductance.

[0057] The stub acts as a conductive path, electrically connecting the circular radiating patch and the folded grounding patch. When the total current flowing through the stub remains constant, reducing the width of the stub enhances the current concentration at the stub location. After the current concentration effect occurs, the equivalent resistance and equivalent inductance parameters of the stub increase accordingly, thereby changing the overall circuit electrical characteristics of the antenna.

[0058] The input impedance of the antenna at 0.915 GHz is 3.96 + j191 Ω.

[0059] At the operating frequency of 0.915 GHz, the simulated input impedance of the antenna is 3.96 + j191 Ω, where the real part 3.96 Ω represents the equivalent radiation resistance of the antenna, and the imaginary part j191 Ω represents the strong inductive reactance of the antenna. This impedance result reflects the electrical input characteristics of the antenna at this frequency, and the maximum power transfer factor is 0.81.

[0060] At 0.915 GHz, the input impedance calculated by electromagnetic simulation and equivalent circuit model is basically consistent, and the resistance variation trend and resonance position are also consistent. This indicates that the equivalent circuit can effectively describe the resonance and impedance matching mechanism formed by the circular radiating patch, complementary sawtooth gap and short stubs on both sides, and verifies the rationality of the simulation results.

[0061] Formula for calculating the power transfer coefficient τ between the antenna and the chip:

[0062]

[0063] in, The input impedance of the tag antenna. This refers to the chip's input impedance. (·) indicates taking the real part of the impedance.

[0064] The power transfer coefficient represents the efficiency of power transfer from the antenna to the chip. The coefficient reaches its maximum value when the antenna impedance and the chip impedance are conjugate matched, at which point the most efficient power transfer can be achieved between the antenna and the chip.

[0065] The tag antenna also includes an equivalent circuit model, which equates the complementary radiating patch to a parallel resonant branch, the stub to a series resistor and a series inductor, and the complementary sawtooth slot to a slot capacitance connected across the input terminal. The input impedance is expressed as:

[0066]

[0067]

[0068]

[0069]

[0070]

[0071] in, The input impedance of the tag antenna; and These are the equivalent impedances of the two complementary radiating patches, respectively. This is the total series impedance of the two short stubs; The equivalent capacitive reactance for complementary sawtooth gaps; , This represents the radiation and loss resistance of the two radiating patches. , This represents the corresponding equivalent inductance. , This represents the equivalent capacitance between the radiating patch and the grounding plate. and These represent the total resistance and total inductance of the two short-circuited wires, respectively. This represents the equivalent capacitance of the sawtooth slit. It represents angular frequency.

[0072] The final input impedance parameters of the tag antenna can be obtained by analyzing the above calculation formula.

[0073] An electromagnetic simulation model of a circular folded patch tag antenna was established, with the tag placed at the center of a 200mm × 200mm metal plate. The simulation structure included a flexible polyimide substrate, a circular radiating patch, complementary sawtooth slots, a U-shaped slot, short stubs on both sides, a circular grounding plate, a foam dielectric layer, and an RFID chip. The simulation process sequentially employed a straight-slot base structure, a structure incorporating complementary sawtooth slots, and a structure with both complementary sawtooth slots and U-shaped slots to compare the effects of different structures on the resonant frequency and input impedance.

[0074] When using a straight-slit structure, the radiating patches on both sides mainly exhibit capacitive behavior, resulting in insufficient inductive compensation, and the tag resonant frequency is 1.134 GHz. After replacing the straight-slit with a complementary sawtooth slot, the current path in the feeding region is significantly extended, and the sawtooth edges generate strong current convergence and equivalent inductance, reducing the tag resonant frequency to 0.926 GHz. After further adding a U-shaped slot, the local current flows around the U-shaped slot, and the additional inductance further reduces the resonant frequency to 0.915 GHz. At this point, the antenna input impedance is approximately 3.96 + j191 Ω, forming a good conjugate match with the chip's capacitive impedance.

[0075] The surface current distribution at 915 MHz shows that the current mainly flows along both sides of the complementary sawtooth gap, around the U-shaped gap, and along the short stubs on both sides. The current density is higher at the sawtooth edges and short stubs, proving that the above structure does indeed introduce a significant inductive effect. Meanwhile, the current around the circular radiating patch is still continuously distributed along the circumference, indicating that the tuning structure in the central region does not significantly cut off the main radiating current path.

[0076] The influence of structural parameters shows that extending the sawtooth current path or reducing the sawtooth gap width will increase the equivalent inductance of the feeding region and lower the resonant frequency; reducing the stub width will increase the equivalent resistance and equivalent inductance of the stub, with the input reactance changing more significantly; increasing the effective width of the U-shaped gap or extending the U-shaped current path will fine-tune the resonant frequency, while the power transfer coefficient at the resonant point will change relatively little. Therefore, coarse tuning can be achieved first using complementary sawtooth gaps and stubs, and then fine matching can be achieved using U-shaped gaps.

[0077] An equivalent circuit is established based on the electromagnetic effects of each component of the tag antenna. The two complementary radiating patches are characterized by parallel resistor, inductor, and capacitor branches, respectively. The resistor reflects radiation and conductor loss, the inductor reflects the inductive contribution of the current path on the patch surface, and the capacitor reflects the coupling between the radiating patch and the ground plate. The short stubs on both sides are characterized by series resistor and inductor. The complementary sawtooth gap is characterized by gap capacitance, thus obtaining the input impedance of the tag antenna.

[0078] The equivalent capacitance between the radiating patch and the grounding plate is calculated based on the capacitance relationship of parallel plates. The stub resistance takes into account the resistivity of the copper conductor, the skin depth, and the current congestion effect. The stub inductance is calculated based on the inductance model of a planar rectangular conductor. The equivalent capacitance of the complementary sawtooth gap is obtained based on the total gap length, gap width, and dielectric layer thickness. The equivalent resistance and inductance of the radiating patch branch are obtained by fitting the simulated impedance curve.

[0079] Comparing the calculated results with the simulation results, at 915MHz, the input impedance obtained from the equivalent circuit model almost coincides with the input impedance obtained from the simulation, and the trends of resistance and reactance change are consistent within the target frequency band. This result further demonstrates that the inductive loading provided by the complementary sawtooth slot and the stubs on both sides, the capacitive coupling between the radiating patch and the grounding patch, and the slot coupling effect can be accurately described by the established equivalent circuit, thus verifying the antenna structure design and simulation results at the circuit level.

[0080] Tag antenna samples were fabricated, and their read performance was tested using the Voyantic Tagformance Pro testing system. Before testing, the system was calibrated using a reference tag to determine the forward link loss, including test cable loss and free space propagation loss. The tag under test was placed on a metal plate or metal container surface, and a threshold power scan was used to determine the minimum transmit power required for the chip to be activated by the reader. The maximum read distance of the tag is expressed by the following formula:

[0081]

[0082] In the formula, For maximum reading distance, The wavelength corresponding to the test frequency. The equivalent isotropic radiated power of the reader / writer. The gain of the tag antenna in the direction of the reader. This refers to the power transfer coefficient between the antenna and the chip. This represents the minimum activation power corresponding to the chip's read sensitivity.

[0083] Under 4W EIRP conditions, the tag was installed at the center of 200mm×200mm and 100mm×100mm aluminum plates, respectively, and the maximum reading distances were measured to be 14.3m and 13.56m, respectively; the maximum reading distance under free space conditions was 8.4m. Directional reading tests showed that the tag exhibited an approximately figure-eight reading pattern in the xy plane, and achieved maximum reading distances of approximately 12.1m and 13.5m in the dominant directions of the xz and yz planes, respectively.

[0084] The tags were affixed to the surfaces of rectangular steel containers, cylindrical aluminum containers, and cylindrical steel containers for testing. The maximum reading distance on the cylindrical aluminum container was approximately 11.35 m; the maximum reading distance on the metal container, which has relatively lower reading performance, was still approximately 9 m. Although the material, size, and surface curvature of different metal objects caused resonant frequency shifts, the tags maintained a reading distance of no less than 8 m in the 905 MHz to 925 MHz frequency band, verifying the isolation effect of the circular grounding plate and foam dielectric layer on the metallic environment, as well as the adaptability of various inductive tuning structures to changes in the metal plateau.

[0085] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A metal environmental RFID tag antenna integration system without through-hole structure, characterized in that, It includes a flexible substrate, which is provided with a metal conductor pattern, a dielectric layer and a radio frequency identification chip; The metal conductor pattern, in its unfolded state, includes a circular radiating patch in the center, grounding plates on both sides, and a short stub connecting the circular radiating patch and the grounding plates. The circular radiating patch includes complementary radiating patches with complementary sawtooth gaps between them, and the radio frequency identification chip is connected between the feed terminals of the two radiating patches. One of the radiating patches has a U-shaped slit located near the chip; The flexible substrate is folded along the short stubs on both sides and then wrapped around the surface of the dielectric layer, so that the circular radiating patch is located on one side of the dielectric layer and the two grounding patches are located on the other side of the dielectric layer, forming a folded patch tag antenna suitable for mounting on a metal surface. The stub provides a return path to the grounding plate for the circular radiating patch, and the antenna does not contain metallized vias.

2. The through-hole-free metal environmental RFID tag antenna integration system according to claim 1, characterized in that, The flexible substrate is a flexible polyimide substrate; The metal conductor pattern is formed by shaping and folding a flexible polyimide copper-clad layer.

3. The through-hole-free metal environmental RFID tag antenna integration system according to claim 1, characterized in that, The dielectric layer is a foam dielectric layer, used to maintain the circular shape of the label and determine the spacing between the circular radiating patch and the grounding plate.

4. The through-hole-free metal environmental RFID tag antenna integration system according to claim 1, characterized in that, The patch tag antenna is cylindrical, with a diameter of 32mm and a thickness of 3mm.

5. The through-hole-free metal environmental RFID tag antenna integration system according to claim 1, characterized in that, The complementary sawtooth gap is formed by the folded edges of two interlocking radial patches, which is used to extend the surface current path in the feeding area and introduce equivalent inductance to adjust the resonant frequency.

6. The through-hole-free metal environmental RFID tag antenna integration system according to claim 1, characterized in that, The U-shaped slit is positioned in the region of one of the radiating patches near the chip to extend the local surface current path and introduce additional inductance to adjust the resonant frequency and input reactance.

7. The through-hole-free metal environmental RFID tag antenna integration system according to claim 1, characterized in that, The stubs connect the circular radial patch to the folded grounding plate respectively. Reducing the width of the stubs will increase the current concentration at that point, thereby increasing the equivalent resistance and equivalent inductance.

8. The through-hole-free metal environmental RFID tag antenna integration system according to claim 1, characterized in that, The input impedance of the antenna at 0.915 GHz is 3.96 + j191 Ω.

9. The through-hole-free metal environmental RFID tag antenna integration system according to claim 1, characterized in that, The tag antenna also includes an equivalent circuit model, which treats the complementary radiating patch as a parallel resonant branch, the stub as a series resistor and a series inductor, and the complementary sawtooth slot as a slot capacitor connected across the input terminal. The input impedance is expressed as: in, The input impedance of the tag antenna; and These are the equivalent impedances of the two complementary radiating patches, respectively. This is the total series impedance of the two short stubs; The equivalent capacitive reactance for complementary sawtooth gaps; , This represents the radiation and loss resistance of the two radiating patches. , This represents the corresponding equivalent inductance. , This represents the equivalent capacitance between the radiating patch and the grounding plate. and These represent the total resistance and total inductance of the two short-circuited wires, respectively. This represents the equivalent capacitance of the sawtooth slit. It represents angular frequency.

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