Method for predicting resonant frequency of a spiral resonator, dimensional analysis method and device

Abstract

The present disclosure relates to a method for predicting the resonant frequency of a spiral resonator, a size analysis method and device, belonging to the field of radio frequency electronic engineering and quantum precision measurement. The method for predicting the resonant frequency of the spiral resonator comprises: dividing the main coil of the spiral resonator into a plurality of sub-segments to establish a mutual inductance matrix based on the plurality of sub-segments; obtaining the total equivalent inductance of the spiral resonator based on the mutual inductance matrix; constructing a multi-body coupled capacitance network model according to a plurality of capacitance components of the spiral resonator; obtaining the total equivalent capacitance of the spiral resonator based on the multi-body coupled capacitance network model; and determining the predicted value of the resonant frequency of the spiral resonator according to the total equivalent inductance and the total equivalent capacitance. The present disclosure can obtain a more accurate predicted value of the resonant frequency, and provide more accurate parameters for the design, manufacture and processing of the spiral resonator.

Description

Technical Field

[0001] This disclosure generally relates to the fields of radio frequency electronic engineering and quantum precision measurement, and particularly to a method, dimensional analysis method and apparatus for predicting the resonant frequency of a spiral resonator. Background Technology

[0002] A spiral resonator is a radio frequency (RF) resonant element with a cavity coaxial transformer structure. The cavity includes a primary coil and a secondary coil. The primary coil receives RF power from the RF source and transmits it to the secondary coil via electromagnetic coupling. The secondary coil is electrically connected to the load through its output terminal, forming a resonant circuit. Spiral resonators achieve frequency selection, impedance matching, and energy storage by using the highest possible quality factor (Q value) and miniaturized design. Spiral resonators can be applied in quantum information processing, precision spectral analysis, and high-resolution mass spectrometry. For example, ion traps, as core devices in quantum information processing and precision spectroscopy, rely on the strong oscillating electric field generated by RF electrodes, requiring a spiral resonator to convert the driving power into 100-1000 volt RF voltage. The Q value, or quality factor, is a core parameter measuring the energy storage efficiency and loss level of a spiral resonator. It is defined as the ratio of the total energy stored in the resonator to the energy lost per cycle, or its equivalent expression, such as the ratio of reactance to resistance, or the ratio of center frequency to bandwidth. A higher Q value indicates that the resonator has less energy loss, higher energy storage efficiency, sharper resonance characteristics, and better selectivity.

[0003] The resonant frequency is a crucial parameter to consider when designing, manufacturing, and processing helical resonators, significantly impacting their suitability for various applications. Existing algorithms for predicting the resonant frequency of helical resonators exhibit low accuracy and cannot perform dynamic tolerance analysis on the resonator's dimensions. Specifically, on one hand, existing algorithms ignore complex interference between coils (mutual inductance effects) and multi-component capacitance, resulting in a difference of over 10% between the predicted resonant frequency and the actual resonant frequency after the helical resonator is manufactured, leading to low prediction accuracy. Existing empirical formulas (such as the Medhurst formula) were developed decades ago for standard coils, rendering them ineffective if the coil pitch is uneven or the structure is unique. On the other hand, existing prediction methods can only calculate the resonant frequency under static dimensions, failing to quantify the sensitivity of processing tolerances (such as slight diameter variations caused by copper wire springback and pitch stretching) to frequency drift. This forces processing to rely on guesswork and trial and error, hindering high-precision manufacturing. Summary of the Invention

[0004] To overcome several problems existing in the prior art, this disclosure provides a method, a size analysis method, and an apparatus for predicting the resonant frequency of a spiral resonator.

[0005] According to some embodiments of this disclosure, a method for predicting the resonant frequency of a spiral resonator is provided, comprising: dividing the main coil of the spiral resonator into multiple segments to establish a mutual inductance matrix based on the multiple segments; obtaining the total equivalent inductance of the spiral resonator based on the mutual inductance matrix; constructing a multi-body coupled capacitor network model based on multiple capacitance components of the spiral resonator; obtaining the total equivalent capacitance of the spiral resonator based on the multi-body coupled capacitor network model; and determining the predicted value of the resonant frequency of the spiral resonator based on the total equivalent inductance and the total equivalent capacitance.

[0006] According to some embodiments of this disclosure, an apparatus for predicting the resonant frequency of a spiral resonator is provided, comprising: a total equivalent inductance acquisition module, a total equivalent capacitance acquisition module, and a resonant frequency prediction value determination module. The total equivalent inductance acquisition module is configured to divide the main coil of the spiral resonator into multiple segments to establish a mutual inductance matrix based on the multiple segments, and to acquire the total equivalent inductance of the spiral resonator based on the mutual inductance matrix. The total equivalent capacitance acquisition module is configured to construct a multi-body coupled capacitor network model based on multiple capacitance components of the spiral resonator, and to acquire the total equivalent capacitance of the spiral resonator based on the multi-body coupled capacitor network model. The resonant frequency prediction value determination module is configured to determine the predicted value of the resonant frequency of the spiral resonator based on the total equivalent inductance and the total equivalent capacitance.

[0007] According to some embodiments of this disclosure, a method for analyzing the size of a helical resonator is provided, comprising: establishing a resonant frequency prediction model using the aforementioned method for predicting the resonant frequency of a helical resonator; establishing a partial differential model of the size parameter of the helical resonator to be analyzed with respect to the resonant frequency based on the resonant frequency prediction model; obtaining a sensitivity coefficient for the size parameter to be analyzed based on the partial differential model; and performing a sensitivity analysis of the size parameter to be analyzed based on the resonant frequency of the helical resonator based on the sensitivity coefficient.

[0008] According to some embodiments of this disclosure, a helical resonator size analysis device is provided, including: a resonant frequency prediction module, a sensitivity coefficient acquisition module, and a sensitivity analysis module. The resonant frequency prediction module is configured to establish a resonant frequency prediction model using the aforementioned method for predicting the resonant frequency of a helical resonator. The sensitivity coefficient acquisition module is configured to establish a partial differential model of the helical resonator's size parameter to be analyzed regarding the resonant frequency based on the resonant frequency prediction model, and to obtain a sensitivity coefficient regarding the size parameter to be analyzed based on the partial differential model. The sensitivity analysis module is configured to perform sensitivity analysis of the helical resonator's resonant frequency on the size parameter to be analyzed based on the sensitivity coefficient.

[0009] The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects:

[0010] The method and apparatus for predicting the resonant frequency of a spiral resonator disclosed herein can accurately describe the strong inter-turn coupling effect and obtain a more accurate total equivalent inductance of the spiral resonator; considering the multi-component capacitance of the spiral resonator, a more accurate total equivalent capacitance of the spiral resonator is obtained, and further a more accurate resonant frequency prediction value is obtained, providing more accurate parameters for the design, manufacture and processing of spiral resonators.

[0011] The spiral resonator dimensional analysis method and apparatus disclosed herein can perform dimensional analysis on various dimensional parameters of spiral resonators, providing parameter guidance for the design, manufacturing and processing of high-precision spiral resonators. Attached Figure Description

[0012] To more clearly illustrate the technical solutions of this disclosure, the embodiments of this disclosure will be further explained and described with reference to the following drawings. These drawings are only used to more conveniently and specifically describe the embodiments of this disclosure and are not intended to limit this disclosure.

[0013] Figure 1 This is a flowchart illustrating a method for predicting the resonant frequency of a spiral resonator according to some embodiments of the present disclosure;

[0014] Figure 2 This is a schematic diagram of a helical resonator with a single main coil structure according to some embodiments of the present disclosure;

[0015] Figure 3 This is a schematic diagram illustrating a complex mutual inductance coupling between segments according to some embodiments of this disclosure;

[0016] Figure 4 This is a schematic diagram illustrating the mutual inductance matrix elements and self-inductance term correction according to some embodiments of this disclosure;

[0017] Figure 5 This is a schematic diagram of a helical resonator with a dual main coil structure according to some embodiments of the present disclosure;

[0018] Figure 6 This is a simulation model diagram of a helical resonator with a dual main coil structure, shown according to some embodiments of this disclosure;

[0019] Figure 7 This is a schematic diagram of capacitor components connected in parallel according to some embodiments of this disclosure;

[0020] Figure 8 This is a bottom view of a dual main coil inside a shield, as shown in some embodiments of this disclosure;

[0021] Figure 9 This is a bottom view of the shielding cover shown according to some embodiments of the present disclosure;

[0022] Figure 10 This is an external view of a spiral resonator equipped with a coupling adjustment mechanism, shown according to some embodiments of the present disclosure;

[0023] Figure 11 This is a side view of a coupling adjustment mechanism equipped with a primary coil, shown according to some embodiments of the present disclosure;

[0024] Figure 12 This is a schematic diagram showing the arrangement of grounding pad, cage plate and radio frequency signal source connector according to some embodiments of the present disclosure;

[0025] Figure 13 This is a top view of a coupling adjustment mechanism equipped with a primary coil, as shown in some embodiments of this disclosure;

[0026] Figure 14 This is a schematic diagram of an apparatus for predicting the resonant frequency of a spiral resonator, according to some embodiments of the present disclosure;

[0027] Figure 15 This is a flowchart illustrating a method for analyzing the dimensions of a spiral resonator according to some embodiments of this disclosure; and

[0028] Figure 16 This is a schematic diagram of a spiral resonator size analysis device according to some embodiments of the present disclosure. Detailed Implementation

[0029] Some embodiments of this disclosure will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. Various changes, modifications, and equivalents of the methods, apparatus, and / or systems described herein will become readily apparent upon understanding this disclosure. For example, the order of operations described herein is merely illustrative and is not limited to those orders set forth herein, but can be changed as will become readily apparent upon understanding this disclosure, except for operations that must be performed in a particular order. Furthermore, for clarity and brevity, descriptions of features known in the art may be omitted.

[0030] The embodiments described in the following examples of this disclosure are not representative of all embodiments consistent with this disclosure. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this disclosure as detailed in the appended claims. In this disclosure, the main coil refers to the secondary coil of a helical resonator, and the small coil refers to the primary coil of a helical resonator.

[0031] This disclosure provides a method 100 for predicting the resonant frequency of a spiral resonator, the process of which is as follows: Figure 1 As shown, it includes steps S101 to S103.

[0032] Step S101: Divide the main coil of the spiral resonator into multiple sub-segments to establish a mutual inductance matrix based on the multiple sub-segments; based on the mutual inductance matrix, obtain the total equivalent inductance of the spiral resonator.

[0033] The traditional lumped-element model is used to determine the total equivalent inductance of a spiral resonator, which is often used for applications such as... Figure 2 The single-coil (single main coil) structure shown does not fully consider the effects of inter-turn mutual inductance and parasitic load, and is not suitable for helical resonators with two or more main coils. Furthermore, the model fails to effectively cover the unique "common-differential" coupling design in a fully symmetrical dual-main-coil structure, which is prone to generating large systematic errors. Figure 2 The single-main-coil spiral resonator 200 shown includes a shield 201, a main coil 202, an output line 203, a small coil 204, an input line 205, and a BNC (Bayonet-Neill-Concelman) connector 206. One end of the main coil 202 is connected to the output line 203, and the other end is connected to the BNC connector 206 on the wall of the shield 201. One end of the small coil 204 is connected to the wall of the shield 201, and the other end is connected to the RF source input line 205. The RF signal is input to a load such as an ion trap through the output line 203.

[0034] Using the existing solenoid approximation formula ignores the mutual inductance contribution between non-adjacent turns and the magnetic field vector deflection caused by the helix angle, resulting in a large error in the resonant frequency calculation under low number of turns and large pitch design.

[0035] To obtain a more accurate total equivalent inductance, a mutual inductance matrix based on multiple sub-segments is established, including: determining the mutual inductance between each sub-segment and the self-inductance of each sub-segment based on the coil radius and wire diameter of each sub-segment; wherein, when determining the self-inductance of each sub-segment, the axial distance between sub-segments is corrected based on the self-geometric average distance of the sub-segments, and the self-inductance of each sub-segment is determined based on the corrected axial distance; and a mutual inductance matrix based on multiple sub-segments is constructed based on the mutual inductance between each sub-segment and the self-inductance of each sub-segment.

[0036] In some embodiments, based on Maxwell's equations, a discretization strategy using Green's function is employed to discretize the main coil into N current elements, where N is a positive integer representing the total number of coil segments. Each current element corresponds to a current vector in one of the coil segments. The complex mutual inductance coupling between the coil segments is then calculated. This is used to construct an N×N dimensional generalized inductance matrix, which serves as the basis for achieving high-precision prediction. For example... Figure 3 As shown, This represents the mutual inductance between the i-th and j-th coil segments; i and j represent the row and column indices of the segments in the mutual inductance matrix, respectively, and i and j are natural numbers from 1 to N; specifically, when i equals j, it represents the self-inductance of the corresponding coil segment. This is achieved by discretizing the double-helix coil into N current elements and calculating the complex mutual inductance coupling between the coil segments. It can cover the mutual inductance between coil turns of the entire spiral resonator, improving the coil inductance data acquisition capability. The generalized mutual inductance matrix is ​​a specific form of the mutual inductance matrix in step S101. The generalized meaning is that it has a wide range of applications, not limited to the shape and number of coils. It is applicable to single main coil, dual main coil, multi-main coil, and also applicable to dual main coil structures with "common ground-differential" coupling design.

[0037] In some embodiments, such as Figure 3 As shown, the coil is divided into hundreds of segments, and the magnetic field influence of each segment on each of the other segments is calculated. A generalized mutual inductance matrix is ​​constructed using a discretization integration strategy based on the vector magnetic potential Green's function. , Indicates the permeability of vacuum. and These represent two distinct closed integration paths, along which the entire integration proceeds. and They represent along the path and The coordinate parameters are used to describe the position of any point on the line. and These are vector differentials, representing the values ​​along the path. and Take infinitesimal line elements, It is the differential symbol. This represents the radius of the i-th sub-segment. This represents the radius of the j-th sub-segment, which can also be understood as... and They are line elements and The position vector in space. Considering the helical coil as a coupled system composed of N discrete circular loops, the current distribution vector is defined. , , Representing an N-dimensional real space, in resonant mode it is assumed that the current amplitude of each turn is equal. Let T be the transpose matrix symbol. Then the total magnetic energy of the spiral resonator system is... The mutual inductance matrix M represents: ,in, yes A 1xN transpose matrix, M is an N x 1 matrix, and M is an N x N mutual inductance matrix. The elements of the mutual inductance matrix are... , This represents the total equivalent inductance of the spiral resonator. The algebraic sum of all elements of the mutual inductance matrix M: .

[0038] In some embodiments, when the main coil of the spiral resonator is a dual-main-coil structure symmetrical about the axis of the spiral resonator, the total equivalent inductance of the spiral resonator is obtained based on the mutual inductance matrix. This includes: utilizing the symmetry of the dual coils, decomposing the N-row N-column mutual inductance matrix into a symmetric matrix and an antisymmetric matrix, and calculating based on the symmetric matrix and the antisymmetric matrix respectively. The computational workload is reduced by half compared to calculating the mutual inductance matrix, and the total equivalent inductance of the spiral resonator can be obtained faster.

[0039] Furthermore, in some embodiments, based on Maxwell's coaxial toroidal inductance formula and LVKING's arithmetic-geometric mean method, the summation of inter-turn mutual inductance is considered, such as... Figure 4 As shown, the elements of the mutual inductance matrix are calculated using the following formula. ,

[0040] ,in, This represents the vacuum permeability; in this embodiment, the value is [value to be inserted here]. , This represents the radius of the i-th sub-segment. This represents the radius of the j-th sub-segment. In this embodiment, and The value is 26.5mm. Let represent the geometric modulus with respect to the i-th and j-th sub-segments. Let i represent the complete elliptic integral of the first kind with respect to the i-th and j-th subsegments. Let i represent the complete elliptic integral of the second kind with respect to the i-th and j-th subsegments. Let represent the axial coordinate of the projection of the i-th sub-segment onto the axis of the helical resonator. Let represent the axial coordinate of the projection of the j-th sub-segment onto the axis of the helical resonator. Let be the axial distance between the i-th sub-segment and the j-th sub-segment. This represents the square of the axial distance between the i-th sub-segment and the j-th sub-segment.

[0041] Furthermore, using the above formula, since the coil segment itself is a solid cylindrical conductor and the coil itself has a cross-section, the mutual inductance matrix elements are calculated. When the self-induction term (i=j) is, such as Figure 4As shown, the axial distance between coil segments is corrected by the geometric mean distance R of the coil, using the square root of the distance. Replace the above formula ,in, , Indicates the diameter of the main coil wire. This represents the natural constant. If the coil segment is hollow, then... Power of 0 The geometric modulus of the self-inductance coil segments is calculated based on the corrected axial distance, ensuring the accuracy of the diagonal elements in the mutual inductance matrix.

[0042] In some embodiments, to obtain a spiral resonator with a unique frequency band and facilitate 1 / 4 impedance matching of the transmission line, the total length of the main coil needs to be constrained when designing the spiral resonator dimensions. Within the total length of the main coil... Main coil height When both are fixed values, the diameter d of the main coil and the pitch... The number of turns N of the main coil is calculated using the following formula for different given values. c and the length of the main coil output line , When the spiral resonator has a dual-main-coil structure, the first equation... It is equal to the height b of the dual main coils. Specifically, the precise dimensional parameters can be obtained by inverse code solving in numerical analysis software. These dimensional parameters are used not only for the design and simulation of the helical resonator coil, but also for high-precision resonant frequency prediction in subsequent steps.

[0043] Step S102: Construct a multi-body coupled capacitor network model based on the multiple capacitance components of the spiral resonator; obtain the total equivalent capacitance of the spiral resonator based on the multi-body coupled capacitor network model.

[0044] Based on the multiple capacitance components of the spiral resonator, a multi-body coupled capacitor network model is constructed, including: determining the multiple capacitance components of the spiral resonator according to the multi-body coupling mode of the spiral resonator; and superimposing the multiple capacitance components in parallel to obtain the multi-body coupled capacitor network model.

[0045] Based on the structure and connection method of the spiral resonator, the multi-body coupling mode of the spiral resonator is determined. Multi-body coupling of a single-main-coil spiral resonator involves the energy storage of the main coil itself, the effect of the main coil on the shield, and the capacitance between the main coil output line and the shield. Multi-body coupling of dual-main-coil and multi-main-coil spiral resonators involves not only the energy storage of the main coil itself, the effect of the main coil on the shield, and the capacitance between the main coil output line and the shield, but also the differential output line capacitance between two or more main coil output lines.

[0046] Corresponding to the multi-body coupling mode of a dual-main-coil spiral resonator, in some dual-main-coil embodiments, based on the multi-body coupling mode of the spiral resonator, multiple capacitance components of the spiral resonator are determined, including: when the main coil of the spiral resonator is a dual-main-coil structure symmetrical about the axis of the spiral resonator, the multiple capacitance components include: the self-capacitance of the main coil. Main coil-shielding capacitor Output line - shielding capacitor and differential output line inter-capacitance ;like Figure 5 As shown, the aforementioned dual-main-coil spiral resonator 500 includes: a cylindrical shield 501 with a bottom surface, two main coils 502 symmetrically arranged around the spiral resonator axis, a coupling adjustment mechanism 503, and a primary coil 504. The symmetrical dual main coils make the magnetic field distribution within the spiral resonator cavity more uniform and reduce losses, resulting in a significant performance improvement compared to traditional single-coil spiral resonators. Figure 6 This is a simulation model diagram of a helical resonator with a dual master coil structure, as shown in the simulation software.

[0047] When an ion trap system is connected in parallel to the output of a spiral resonator to output an RF signal to the ion trap system, the multiple capacitive components also include the equivalent load capacitance of the ion trap system. The input should be adapted according to the actual application scenario. When the spiral resonator is connected to the load, such as... Figure 7 As shown, the total equivalent capacitance of the spiral resonator It is composed of five independent components connected in parallel and superimposed.

[0048] Traditional spiral resonator designs suffer from the following drawbacks: A single main coil or a non-perfectly symmetrical dual main coil structure leads to uneven electromagnetic field distribution, significant eddy current losses and skin effect losses, limiting Q-value improvement; the coupling adjustment mechanism between the main coil and the bottom coil in traditional spiral resonators has low precision (millimeter-level) and poor stability, failing to achieve micrometer-level precise positioning and long-term stable coupling between the main coil and the bottom coil; improper inter-turn spacing design in dual main coils results in a surge in energy loss and a decrease in energy storage efficiency due to strong near-field coupling, thus negating the Q-value improvement advantage brought by the symmetrical structure; grounding of the main coil and shield relies on solder or additional connectors, leading to high contact resistance, easy oxidation, and low reliability, affecting the resonator's performance stability. These drawbacks limit the overall performance of spiral resonators, making it difficult to improve their Q-value.

[0049] To overcome the aforementioned shortcomings of traditional spiral resonator designs, a spiral resonator 500 with a dual-main-coil structure was adopted. Specifically, as shown... Figure 5As shown, in the above-mentioned dual-main-coil spiral resonator 500, two main coils 502 and a primary coil 504, symmetrical about the axis of the spiral resonator, are located inside a cylindrical shield 501 with a bottom surface. The first ends of the two main coils 502, symmetrical about the axis of the spiral resonator, are used to output radio frequency signals, and the second ends of the two main coils 502, symmetrical about the axis of the spiral resonator, are electrically connected to the inner wall of the shield. The coupling adjustment mechanism 503 includes a radio frequency signal source connector 5031, a retractable lens sleeve, a grounding pad, and a cage plate. The retractable lens sleeve has a grounding pad embedded inside its cylinder, the radio frequency signal source connector 5031 is fixed on the grounding pad, and the retractable lens sleeve is fixed to the bottom surface of the shield 501 through the cage plate. The first end of the primary coil 504 is connected to the radio frequency signal source connector 5031, and the second end of the primary coil 504 is connected to the grounding pad.

[0050] A physical example of a helical resonator with a dual main coil structure, as shown below. Figures 8 to 12 As shown. Figure 8 This is a bottom view of the dual main coils inside the shielding cover, including two symmetrical main coils and a reinforcing support device fixed to the top surface of the shielding cover. This reinforcing support device includes multiple columns fixed to the top surface of the shielding cover. Each column has one end fixedly connected to the top surface of the shielding cover and the other end connected to a supporting ring. Multiple insulating support blocks are symmetrically arranged on the supporting ring. These insulating support blocks support the main coils, helping them maintain stress balance and preventing deformation. Furthermore, multiple layers of insulating support blocks are arranged along the axial direction of the main coils to support main coils at different heights, further maintaining the shape stability of the main coils. For example, in a preferred embodiment, the insulating support blocks can be made of Teflon material; alternatively, materials with good dimensional stability such as polycarbonate and polyphenylene sulfide can also be used.

[0051] In some embodiments, the above-described dual-main-coil spiral resonator employs a "single-coil rotational symmetry" design method, rotating a single main coil 180° around its central axis to form a completely symmetrical dual-main-coil structure. Specific parameters and connection methods include: Figure 5 As shown, the bottom of the dual main coils extends to connect with the shielding cover, forming a grounding terminal, and the top extends to provide an independent output terminal. The spacing w between the center lines of the output lines can be adjusted between 10mm and 30mm. The key parameters of the main coils are: coil diameter d is 30-80mm, and wire diameter... =3mm, coil material can be oxygen-free copper, pure silver, gold, etc., number of turns N c 3-18 turns, main coil pitch The height b of the dual main coil is determined by the number of turns and the pitch, ranging from 8 to 30 mm, and b = N. c•τ; The effective pitch of the dual main coils is half that of the single coil, and the total number of turns of the dual main coils is twice that of the single coil. The helix angle remains constant to ensure a completely symmetrical electromagnetic field distribution, suppressing local eddy current losses at the source. The axial distance from the bottom of the two main coils 502, which are symmetrical about the axis of the helical resonator, to the top surface of the coupling adjustment mechanism 503 is H. To avoid strong inter-turn coupling negating the Q-value advantage, the inter-turn pitch of the dual main coils strictly follows… The diameter should be no less than 1.5 mm. This structure, simulated using HFSS (High Frequency Structure Simulator), has been experimentally verified in the 20-100MHz frequency band, showing a Q value improvement of over 30% compared to traditional single-coil coils, with a maximum improvement of 47%. If the coil is made of pure copper, at 70MHz... With parameters of 55mm and 16mm, the Q value of this dual main coil is 982, compared to the Q value of 666 for the traditional single coil. This dual main coil achieves a larger Q value at room temperature.

[0052] Furthermore, in some embodiments, the three-main-coil spiral resonator employs a "single-coil rotational symmetry" design method, rotating a single main coil around its central axis by 120° and 240° to form a completely symmetrical three-main-coil structure. The design of spiral resonators with a larger number of main coils follows the same concept, with multiple main coils symmetrically arranged around an axis to achieve better electromagnetic distribution, reduce energy loss, and improve the Q value.

[0053] In some embodiments, the coupling adjustment mechanism of the above-mentioned dual-main-coil spiral resonator 500 is a stable micron-level coupling adjustment mechanism obtained by custom modification of a retractable standard optical lens sleeve. The specific structure is shown in the figure below. The retractable lens sleeve and the standard optical cage plate are combined, and a custom-embedded thin metal (stainless steel) gasket is added. The diameters of the three are matched. The small coil is fixed to the inner core of the SMA (Sub-Miniature A) connector by welding at one end and welded to the SMA gasket at the other end to achieve grounding and ensure the continuity of signal transmission. The axial distance between the main coil and the small coil can be adjusted within the sleeve's telescopic range (0-15mm) with an accuracy of ±0.1μm, which meets the high coupling accuracy requirements of the spiral resonator and the ion trap.

[0054] In some embodiments, the spiral resonator 500 with the above-mentioned dual main coil structure achieves stable grounding by optimizing the grounding method at the connection between the main coil and the shield through soldering process, as follows: the solder is a high-conductivity silver-tin alloy (silver content 3.5%, melting point 217℃), the main coil is oxygen-free copper wire (conductivity ≥99.99%), the shield is made of oxygen-free copper, and the grounding contact surface is pre-polished with sandpaper to remove the oxide layer (roughness Ra≤0.8μm); hot air gun welding is used, with hot air temperature 300±10℃ and wind speed 3-5m / s, and the silver-tin alloy solder is evenly filled into the contact area between the bottom of the main coil and the shield, with a welding area ≥15mm², ensuring no false soldering or bubbles; anti-oxidation treatment: after welding, a 0.5-1mm thick silicone thermally conductive anti-oxidation coating (dielectric strength ≥20kV / mm) is coated at the grounding connection to isolate air and moisture and prevent the solder layer from oxidizing and failing.

[0055] Furthermore, in some embodiments, the grounding method at the connection between the main coil and the shield is improved by adopting an integrated manufacturing structure to further enhance grounding stability and service life. Specifically, this includes: the main coil uses high-conductivity oxygen-free copper wire with a wire diameter of... =3mm; the shielding cover is made of oxygen-free copper of the same material, and both have the same coefficient of thermal expansion to avoid cracking and deformation due to thermal stress after molding; such as Figure 9 As shown, the bottom of the shield has a pre-set arc-shaped matching groove with a groove radius equal to the radius of the main coil copper wire plus 0.1mm, ensuring a tight fit between the copper wire and the groove; the inner wall of the groove is plated with 5-10μm. A thick silver layer (purity ≥99.9%) reduces contact resistance and prevents oxidation. The integrated connection section at the bottom of the main coil is 10-15mm long, ensuring connection stability without interfering with the electromagnetic field distribution. This integrated connection section refers to the copper wire segment extending from the bottom coil of the main coil and connecting to the shield wall. In the manufacturing process, the shield is precision die-cast with a mold accuracy of ±0.02mm, ensuring the coaxiality of the groove is ≤0.03mm, and the batch production yield is ≥98%. The bottom section of the wound main coil is embedded into the groove of the shield and fixed by a positioning fixture. A hot-pressing process (temperature 220±10℃, pressure 12±2MPa, holding time 30±5s) is used to achieve an integrated connection. After connection, a laser rangefinder is used to ensure that the coaxiality error between the main coil and the shield is ≤0.05mm, and the impact of this deviation on the resonant frequency is ≤0.1MHz, within the predicted error range (<5%). The grounding resistance is ≤0.01. The connection strength is ≥15MPa; after a simulated aging test at 85℃ and 85% humidity for 1000 hours, the expected long-term (10 years) grounding resistance change is ≤0.002. Compared with the soldering process optimization solution, the integrated manufacturing structure solution improves grounding stability by 80% and reduces eddy current loss by 15%.

[0056] In some embodiments, the self-capacitance of the main coil Main coil-shielding capacitor Output line - shielding capacitor and differential output line inter-capacitance It can be obtained through the following methods:

[0057] Based on Medhurst theory and introducing the helix angle The corrected formula, ,in, Represents the vacuum permittivity, with a value of . N c This indicates the number of turns in a single main coil, where d represents the diameter of the main coil. Indicates the helix angle. , 'b' represents the pitch of the main coil, and 'b' represents the height of the dual main coils. In this embodiment, 'b' = 80.26 mm. , and The structural coefficients are obtained through fitting calculations. , and The values ​​are 0.717439, 0.933048, and 0.106, respectively. The helix angle is introduced. Then, the magnetic field vector deflection caused by the helix angle was taken into account, which avoided large calculation errors of the resonant frequency under low number of turns and large pitch design.

[0058] The formula for coaxial cylindrical capacitance is adopted, and the effective diameter is introduced. Correcting edge field effects ,in, Indicates the diameter of the main coil wire. Indicates the effective main coil diameter. , To account for the equivalent diameter length caused by the bulge due to coil winding, D represents the inner diameter of the shield. In this embodiment, D is 104 mm.

[0059] Output line - shielding capacitor This is used to describe the parasitic capacitance between the top output line of the main coil and the shield. This indicates the length of the main coil output line.

[0060] Since there are two parallel output leads at the top of the dual main coils, forming a two-wire transmission line structure, this capacitance cannot be ignored. Therefore, the inter-line capacitance of the differential output lines needs to be considered. , Among them, arccosh Let w represent the inverse hyperbolic cosine function, and w represent the center-to-center distance between the parallel output lines of the two main coils. In this embodiment, w is 10 mm. It is 3mm.

[0061] In some embodiments, the total equivalent capacitance of the spiral resonator is obtained based on a multi-body coupled capacitor network model, including: the total equivalent capacitance of the dual-main-coil spiral resonator. It is composed of four independent components connected in parallel and superimposed. When a spiral resonator is connected to an ion trap load, , This is the equivalent load capacitance of the ion trap system.

[0062] Step S103: Determine the predicted value of the resonant frequency of the spiral resonator based on the total equivalent inductance and total equivalent capacitance.

[0063] In some embodiments, adopt Calculate the predicted resonant frequency of the helical resonator. In this embodiment, the total equivalent inductance of the aforementioned spiral resonator is... Total equivalent capacitance The calculation formula, after substituting the aforementioned parameters, yields the predicted resonant frequency value. Its value is consistent with the HFSS simulation value f. HFSS (77.8MHz) and experimental value f Exp The error for (80.4MHz) is less than 5%, which is more accurate than the error of more than 10% in the resonant frequency prediction value calculated by existing algorithms.

[0064] The method for predicting the resonant frequency of a helical resonator based on a discretization strategy, steps S101, S102 and S103, is applicable to helical resonators with 1, 2, 3 or more main coils, has good scalability, and can be directly adapted to complex designs of non-uniform pitch or variable diameter coils.

[0065] To verify the effectiveness and accuracy of the resonant frequency prediction method based on a discretized mutual inductance matrix and a multi-body coupled capacitor network model proposed in this disclosure, extensive comparative verification experiments covering multiple key radio frequency bands, including 30 MHz, 50 MHz, and 70 MHz, were conducted, with numerous tests performed on both single-main-coil and symmetrical dual-main-coil structures, using various combinations of geometric parameters. The prediction results (F...) pred ) and the reference frequency (F) measured based on high-precision finite element simulation (HFSS) and actual physical experiments. ref A comparison was made, and the relative prediction error was calculated. Among them, the reference frequency F ref It is the simulated value f of the resonant frequency of the spiral resonator.HFSS and experimental value f Exp The calculated value, for example, is the simulation value f. HFSS and experimental value f Exp The average value is used as the reference frequency F ref Alternatively, data processing methods such as multi-point fitting can be used to obtain the simulated value f. HFSS and experimental value f Exp Obtain the reference frequency F ref .

[0066] In the 50MHz band with a single main coil structure, resonant frequency prediction, reference frequency calculation, and comparison were performed on 22 sets of helical resonators with different geometric configurations. The mean absolute error (MAE) of the resonant frequency prediction values ​​was only 4.16%. Within the optimal geometric parameter range, the prediction error of the corresponding resonant frequency prediction values ​​was less than 1%. For example, when the main coil diameter d = 50mm and the main coil pitch... When the diameter is 8mm, the predicted resonant frequency deviates from the reference frequency by only 0.05%; when the main coil diameter d = 60mm, the main coil pitch... When the diameter is 9mm, the predicted resonant frequency deviates from the reference frequency by only 0.50%.

[0067] In the 70MHz band with a single main coil structure, the distributed parameter effect intensifies with increasing frequency, but the prediction accuracy of this method actually improves further, with the mean absolute error decreasing to approximately 3.27%. This is particularly evident in the main coil pitch. With a sparse winding configuration of 9 mm, more than 87% of the samples had a prediction error of less than 5%, verifying the superiority of the discretized mutual inductance model in handling high-frequency non-uniform magnetic field distributions.

[0068] The dual-main-coil spiral resonator exhibits a stable average absolute error of 5.7% to 6.6% in its resonant frequency prediction over a wide frequency range of 30 MHz to 70 MHz. This is significantly better than the over 10% error of existing algorithms that ignore complex interference between coils and multi-component capacitance, demonstrating that the proposed "multi-body coupled capacitor network model" can more accurately decouple the complex electromagnetic interactions between coils and between the coil and the shield. Specific typical verification data include: at 70 MHz, for a main coil diameter d = 50 mm and a main coil pitch... The predicted frequency of a dual-main-coil spiral resonator with a diameter d = 7 mm has a prediction error of 3.60%. In the 30 MHz band, the prediction error is 3.60% for a main coil diameter d = 60 mm and a main coil pitch of... The prediction error of the resonant frequency prediction value of the 8 mm dual-main-coil spiral resonator is further reduced to 0.99%.

[0069] The method disclosed herein overcomes the failure problem of traditional semi-empirical formulas under non-standard geometries. Whether in a single-master coil or a complex multi-master coil structure, this method provides high-precision predictions with practical engineering value. The prediction error in the core design region is generally less than 5%, and in some optimized designs, it can reach below 1%, providing more accurate prediction data for the precision design and manufacturing of helical resonators.

[0070] In the method described in this embodiment, the coil is divided into multiple segments, and the magnetic field influence of each segment on other segments is calculated to construct a mutual inductance matrix. This mutual inductance matrix collects the complex interference of mutual inductance between coils. This mutual inductance matrix is ​​applicable to standard coils and coils with uneven pitch or special structures. Based on this mutual inductance matrix, the strong coupling effect between turns can be accurately described, resulting in a more accurate total equivalent inductance of the spiral resonator. According to the multiple capacitance components of the spiral resonator, a multi-body coupled capacitor network model is constructed, considering the multi-component capacitance of the spiral resonator. Based on this multi-body coupled capacitor network model, a more accurate total equivalent capacitance of the spiral resonator is obtained. Based on the more accurate total equivalent inductance and total equivalent capacitance of the spiral resonator, a more accurate resonant frequency prediction value is obtained, providing more accurate parameters for the design, manufacturing, and processing of the spiral resonator.

[0071] Another embodiment of this disclosure provides a device 1400 for predicting the resonant frequency of a spiral resonator, the structure of which is as follows: Figure 14 As shown, it includes: a total equivalent inductance acquisition module 1401, a total equivalent capacitance acquisition module 1402, and a resonant frequency prediction value determination module 1403.

[0072] The total equivalent inductance acquisition module 1401 is used to divide the main coil of the spiral resonator into multiple segments, establish a mutual inductance matrix based on the multiple segments, and obtain the total equivalent inductance of the spiral resonator based on the mutual inductance matrix. The total equivalent capacitance acquisition module 1402 is used to construct a multi-body coupled capacitor network model based on the multiple capacitance components of the spiral resonator, and obtain the total equivalent capacitance of the spiral resonator based on the multi-body coupled capacitor network model. The resonant frequency prediction value determination module 1403 is used to determine the predicted value of the resonant frequency of the spiral resonator based on the total equivalent inductance and the total equivalent capacitance.

[0073] In some embodiments, the above-mentioned module may be configured by combining a computing and storage device that performs a method for predicting the resonant frequency of a helical resonator with sensors, communication devices, etc. Alternatively, depending on the function of the module, a corresponding dedicated device or dedicated system may be customized to realize the necessary functions of the corresponding module.

[0074] Regarding the apparatus in the above embodiments, the specific methods by which each module performs operations and the corresponding technical effects have been described in detail in the embodiments of the method, and will not be elaborated here.

[0075] This disclosure provides a method 1500 for analyzing the dimensions of a spiral resonator, the process of which is as follows: Figure 15 As shown, it includes steps S1501 to S1503.

[0076] Step S1501: Using the aforementioned method for predicting the resonant frequency of a spiral resonator, establish a resonant frequency prediction model.

[0077] In some embodiments, the aforementioned method for predicting the resonant frequency of a spiral resonator is used to establish a resonant frequency prediction model, including: collecting predicted resonant frequencies of spiral resonators with different numbers of main coils and structural characteristics based on the aforementioned method for predicting the resonant frequency of spiral resonators; establishing a classification dataset based on the correspondence between these predicted resonant frequency values, the number of main coils, and structural characteristics, wherein each dataset includes various parameters and corresponding predicted resonant frequencies of spiral resonators with the same number of main coils and similar structural characteristics; determining whether spiral resonators with the same number of main coils belong to those with similar structural characteristics based on the differences in the geometric parameters of the spiral resonators and an adjustable threshold; and fitting the model to each dataset to obtain a resonant frequency prediction model corresponding to each dataset. By fitting multiple resonant frequency prediction models, it is convenient to quickly predict the resonant frequency of spiral resonators with the same number of main coils and similar structural characteristics, facilitate the screening of outliers, and improve the design efficiency of spiral resonators.

[0078] Step S1502: Based on the resonant frequency prediction model, establish a partial differential model of the size parameters of the spiral resonator to be analyzed with respect to the resonant frequency; according to the partial differential model, obtain the sensitivity coefficients of the size parameters to be analyzed.

[0079] Existing methods can only calculate the frequency under static dimensions and cannot quantify the sensitivity of machining tolerances to frequency drift, making it difficult to guide high-precision manufacturing. To solve this technical problem, in step S1502, a partial differential operator is introduced to establish a partial differential model of the resonant frequency with respect to the dimensional parameters of the helical resonator, and the machining error is modeled as a random variable to quantify the impact of the machining error.

[0080] In some embodiments, a resonant frequency is constructed. The function is then used to calculate the derivative (gradient ∇f) for each geometric parameter, resulting in the sensitivity analysis model: , Represents geometric parameters The sensitivity coefficient, The partial differential symbol is used to calculate the sensitivity coefficient by calculating the corresponding Jacobian matrix.

[0081] In some embodiments, key geometric parameters are selected as the dimensional parameters to be analyzed, and corresponding partial differential models are constructed. For example, the coil diameter d is used to construct a model for the resonant frequency. Using a partial differential model as an example, we will illustrate this. .in, It is the sensitivity coefficient with respect to the coil diameter d; This is the inductance sensitivity component, reflecting the change in magnetic flux cross-section caused by the change in coil diameter. The chain rule can be used to differentiate the mutual inductance matrix. The inductance sensitivity component is obtained. It is the capacitive sensitivity component, which mainly characterizes the self-capacitance of the main coil. Main coil-shielding capacitor The diameter d of the coil increases nonlinearly.

[0082] In one specific embodiment, the geometric parameters of the helical resonator with a dual master coil structure include:

[0083] Main coil diameter: d=53mm, range 30mm-80mm;

[0084] Number of turns of main coil: N c =5.733 turns, as mentioned above The inverse solution yields the result;

[0085] Main coil pitch: =14mm, with a value range of 7mm-30mm;

[0086] Main coil wire diameter: =3mm, with a value range of 2mm-6mm. When the radius of the main coil conductor is uniform, the diameter of the main coil sub-segment is equal to the diameter of the main coil.

[0087] Inner diameter of shielding cover: D=104mm, range 100mm-140mm;

[0088] Main coil output line length: =54.737mm, from The inverse solution yields the result;

[0089] The center-to-center distance between the parallel output lines of the two main coils: w = 10mm, with a range of 10mm-20mm;

[0090] Height of the dual master coils: b=N c ·τ=80.26mm, N c Indicates the number of turns in a single main coil;

[0091] Total number of sub-segments , This indicates the number of main coils in the helical resonator. This represents the proportion of each segment's length to a full turn of the main coil. By adjusting this proportion, the total number of segments is made an integer. For example, in... =2, N c With 5.733 turns, if the proportional coefficient is set to 0.028665, then the total number of segments N is 400.

[0092] Based on the geometric parameters of the spiral resonator with the aforementioned dual-main-coil structure, the sensitivity coefficient of the coil diameter can be calculated using this partial differential model in the 70MHz frequency band. ≈1.2MHz / mm, which is the sensitivity coefficient It is approximately 1.2 MHz / mm.

[0093] Step S1503: Based on the sensitivity coefficient, perform sensitivity analysis of the resonant frequency of the spiral resonator for the size parameter to be analyzed.

[0094] Sensitivity coefficient of coil diameter in the 70MHz frequency band of step S1502 In the embodiment with approximately 1.2 MHz / mm, based on the sensitivity coefficient Sensitivity analysis of the coil diameter *d* (≈1.2 MHz / mm) shows that if the copper wire experiences radial springback during processing, causing a 1 mm increase in diameter, the resonant frequency will decrease by approximately 1.2 MHz. Based on this sensitivity analysis, the difference in error accuracy for different dimensions can be known before processing. This allows for the selection of materials and processes that meet or exceed the required error accuracy for dimensions with varying error accuracies, thereby saving processing costs and time. This quantitative indicator directly guides the design of diameter reduction compensation for winding dies, something existing empirical formulas cannot provide. Similarly, sensitivity analysis can be performed on other geometric parameters of the helical resonator to determine the impact of changes in these parameters on the resonant frequency. This allows for setting different error standards for different geometric parameters during the design, manufacturing, and processing of helical resonators, helping to control costs, improve efficiency, and increase yield within the resonant frequency error range. Based on the method 100 for predicting the resonant frequency of a spiral resonator and the spiral resonator size analysis method 1500, not only can the frequency prediction error be controlled within 5%, but it can also calculate the impact of each dimensional tolerance of the spiral resonator on its performance in advance, just like a "physical examination". This guides the factory to process precisely, avoids processing that can only rely on "guessing" and "trial and error", and improves processing efficiency and intelligence.

[0095] Furthermore, in some embodiments, the resonant frequency prediction errors of helical resonators with multiple sets of geometrical parameters are collected. Data analysis is performed on the correlation between different types of geometrical parameters and the resonant frequency prediction errors to screen out geometrical parameter types whose correlation with the resonant frequency prediction errors is higher than a preset threshold. The correlation can be quantified using data indicators of correlation analysis, such as Pearson correlation coefficient, chi-square test, etc. The method disclosed in this paper can not only output a single frequency prediction value, but also sensitively identify the "unstable region" (high error region) and the "high Q value stable region" (low error region) in the design space by the change of error gradient. For example, through the resonant frequency prediction, reference frequency calculation and comparison of helical resonators with multiple geometrical configurations, it was found that the prediction error has a strong correlation with the coil aspect ratio. When the diameter of the main coil increases significantly (e.g., d=80mm) and the aspect ratio decreases, the prediction error shows a non-linear upward trend (about 10%-12%). Using the partial differential model established in step S1502, spiral resonator designers can proactively avoid highly sensitive geometric dimensions based on this data feedback, thereby significantly improving the resonator's manufacturing yield and frequency stability. The spiral resonator dimensional analysis method 1500 provided in this disclosure can obtain sensitivity coefficients for the analyzed dimensional parameters by establishing a partial differential model of the spiral resonator's dimensional parameters related to the resonant frequency. It quantifies the sensitivity of dimensional tolerances (such as slight diameter changes caused by coil wire springback, pitch stretching, etc.) to frequency drift, enabling dimensional analysis of various dimensional parameters of the spiral resonator and providing parameter guidance for the design, manufacturing, and processing of high-precision spiral resonators.

[0096] This disclosure provides a spiral resonator size analysis device 1600, the structure of which is as follows: Figure 16 As shown, it includes: a resonant frequency prediction module 1601, a sensitivity coefficient acquisition module 1602, and a sensitivity analysis module 1603.

[0097] The resonant frequency prediction module 1601 is configured to establish a resonant frequency prediction model using the aforementioned method for predicting the resonant frequency of a helical resonator. The sensitivity coefficient acquisition module 1602 is configured to establish a partial differential model of the helical resonator's dimension parameters to be analyzed regarding the resonant frequency based on the resonant frequency prediction model, and to obtain sensitivity coefficients for the dimension parameters to be analyzed based on the partial differential model. The sensitivity analysis module 1603 is configured to perform sensitivity analysis of the helical resonator's resonant frequency on the dimension parameters to be analyzed based on the sensitivity coefficients.

[0098] In some embodiments, the above-mentioned modules can be configured by combining a computing and storage device that performs the helical resonator size analysis method 1500 with sensors, communication devices, human-computer interaction devices, etc., or, depending on the function of the module, a corresponding dedicated device or dedicated system can be customized to realize the necessary functions of the corresponding module. Regarding the apparatus in the above embodiments, the specific methods of operation of each module and the corresponding technical effects have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0099] In this description, "multiple" means at least two, referring to two or more, such as two, three, etc., unless otherwise explicitly specified. Other quantifiers are similar. The singular forms "a," "the," and "the" are also intended to include the plural forms unless the context clearly indicates otherwise. Furthermore, unless otherwise specified or clearly indicated from the context, the articles "a" and "an" as used in this disclosure and the appended claims are generally understood to mean "one or more."

[0100] It is further understood that the terms "first," "second," etc., are used to describe various types of information, but this information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another, and do not indicate a specific order or degree of importance. In fact, the expressions "first," "second," etc., are completely interchangeable. For example, without departing from the scope of this disclosure, first information can also be referred to as second information, and similarly, second information can also be referred to as first information.

Claims

1. A method for predicting the resonant frequency of a spiral resonator, characterized in that, include: The main coil of the spiral resonator is divided into multiple sub-segments to establish a mutual inductance matrix based on the multiple sub-segments; Based on the mutual inductance matrix, the total equivalent inductance of the spiral resonator is obtained; Based on the multiple capacitance components of the spiral resonator, a multi-body coupled capacitor network model is constructed. Based on the multibody coupled capacitor network model, the total equivalent capacitance of the spiral resonator is obtained; The predicted value of the resonant frequency of the spiral resonator is determined based on the total equivalent inductance and the total equivalent capacitance. The multi-body coupled capacitor network model is constructed based on the multiple capacitance components of the spiral resonator, including: Based on the multi-body coupling mode of the spiral resonator, the multiple capacitive components of the spiral resonator are determined; The multiple capacitance components are connected in parallel and superimposed to obtain the multi-body coupled capacitor network model. The determination of multiple capacitance components of the spiral resonator based on its multi-body coupling mode includes: When the main coil of the spiral resonator is a dual-main-coil structure symmetrical about the axis of the spiral resonator, the plurality of capacitance components include: the self-capacitance of the main coil. Main coil-shielding capacitor Output line - shielding capacitor and differential output line inter-capacitance ; The dual-main-coil spiral resonator includes: two main coils symmetrical about the axis of the spiral resonator, a columnar shield with a bottom surface, a coupling adjustment mechanism, and a primary coil; Wherein, the self-capacitance of the main coil Main coil-shielding capacitor Output line - shielding capacitor and differential output line inter-capacitance It can be obtained through the following methods: ,in, N represents the vacuum permittivity. c This indicates the number of turns in a single main coil, where d represents the diameter of the main coil. Indicates the helix angle. , b represents the pitch of the main coil, and b represents the height of the dual main coils. , and For structural coefficients; ,in, Indicates the diameter of the main coil wire. Indicates the effective main coil diameter. D represents the inner diameter of the shielding cover; ,in, Indicates the length of the main coil output line; Among them, arccosh Let w represent the inverse hyperbolic cosine function, and w represent the center-to-center distance between the parallel output lines of the two main coils.

2. The method according to claim 1, characterized in that, Establishing a mutual inductance matrix based on the multiple sub-segments includes: Based on the coil radius and wire diameter of each sub-segment, determine the mutual inductance between each sub-segment and the self-inductance of each sub-segment; When determining the self-inductance of each segment, the axial distance between the segments is corrected based on the self-geometric mean distance of the segments, and the self-inductance of each segment is determined based on the corrected axial distance. A mutual inductance matrix based on the mutual inductance between each sub-segment and the self-inductance of each sub-segment is constructed.

3. The method according to claim 1, characterized in that, When the main coil of the spiral resonator is a dual-main-coil structure symmetrical about the axis of the spiral resonator, the total equivalent inductance of the spiral resonator is obtained based on the mutual inductance matrix, including: The mutual inductance matrix is ​​decomposed into a symmetric matrix and an antisymmetric matrix, so as to obtain the total equivalent inductance of the spiral resonator based on the symmetric matrix and the antisymmetric matrix.

4. The method according to claim 1, characterized in that, When the output terminal of the spiral resonator is connected to the ion trap system, the plurality of capacitive components also include the equivalent load capacitance of the ion trap system. ; The total equivalent capacitance of the helical resonator with the dual main coil structure It is composed of five independent components connected in parallel and superimposed. .

5. A device for predicting the resonant frequency of a spiral resonator, characterized in that, The device includes: The total equivalent inductance acquisition module is configured to divide the main coil of the spiral resonator into multiple sub-segments to establish a mutual inductance matrix based on the multiple sub-segments, and to acquire the total equivalent inductance of the spiral resonator based on the mutual inductance matrix. The total equivalent capacitance acquisition module is configured to construct a multi-body coupled capacitor network model based on the multiple capacitance components of the spiral resonator, and to acquire the total equivalent capacitance of the spiral resonator based on the multi-body coupled capacitor network model. A resonant frequency prediction value determination module is configured to determine a predicted value of the resonant frequency of the spiral resonator based on the total equivalent inductance and the total equivalent capacitance. The multi-body coupled capacitor network model is constructed based on the multiple capacitance components of the spiral resonator, including: Based on the multi-body coupling mode of the spiral resonator, the multiple capacitive components of the spiral resonator are determined; The multiple capacitance components are connected in parallel and superimposed to obtain the multi-body coupled capacitor network model. The determination of multiple capacitance components of the spiral resonator based on its multi-body coupling mode includes: When the main coil of the spiral resonator is a dual-main-coil structure symmetrical about the axis of the spiral resonator, the plurality of capacitance components include: the self-capacitance of the main coil. Main coil-shielding capacitor Output line - shielding capacitor and differential output line inter-capacitance ; The dual-main-coil spiral resonator includes: two main coils symmetrical about the axis of the spiral resonator, a columnar shield with a bottom surface, a coupling adjustment mechanism, and a primary coil; Wherein, the self-capacitance of the main coil Main coil-shielding capacitor Output line - shielding capacitor and differential output line inter-capacitance It can be obtained through the following methods: ,in, N represents the vacuum permittivity. c This indicates the number of turns in a single main coil, where d represents the diameter of the main coil. Indicates the helix angle. , b represents the pitch of the main coil, and b represents the height of the dual main coils. , and For structural coefficients; ,in, Indicates the diameter of the main coil wire. Indicates the effective main coil diameter. D represents the inner diameter of the shielding cover; ,in, Indicates the length of the main coil output line; Among them, arccosh Let w represent the inverse hyperbolic cosine function, and w represent the center-to-center distance between the parallel output lines of the two main coils.

6. A method for analyzing the dimensions of a spiral resonator, characterized in that, include: A resonant frequency prediction model is established using the method described in any one of claims 1 to 4; Based on the resonant frequency prediction model, a partial differential model of the size parameters of the spiral resonator to be analyzed with respect to the resonant frequency is established. Based on the partial differential model, the sensitivity coefficients for the size parameter to be analyzed are obtained; Based on the sensitivity coefficient, a sensitivity analysis is performed on the resonant frequency of the helical resonator to the dimension parameter to be analyzed.

7. A device for analyzing the size of a spiral resonator, characterized in that, include: A resonant frequency prediction module is configured to establish a resonant frequency prediction model by means of the method described in any one of claims 1 to 4; The sensitivity coefficient acquisition module is configured to establish a partial differential model of the size parameters of the helical resonator to be analyzed with respect to the resonant frequency based on the resonant frequency prediction model, and to obtain the sensitivity coefficient with respect to the size parameters to be analyzed based on the partial differential model. A sensitivity analysis module is configured to perform sensitivity analysis of the helical resonator resonant frequency to the dimension parameter to be analyzed, based on the sensitivity coefficient.

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