Method for calculating total load capacitance of dual-output spiral resonator and application thereof

Abstract

The application provides a total load capacitance calculation method of a two-way output spiral resonator and application thereof, and the total load capacitance calculation method comprises the following steps: obtaining an equivalent distributed capacitance of the resonator, equivalent capacitances of two-way substrate loads at a working frequency, an access path attenuation coefficient, and actual measurement values of two-way applied capacitances, and using the above-mentioned values to calculate the total load capacitance; the access path attenuation coefficient is defined as a ratio of an effective value of the applied capacitance at the working frequency to the actual measurement value thereof. The application also provides a working frequency prediction method, a loaded Q value evaluation method and an amplitude balance debugging method based on the total load capacitance. By decoupling the two-way substrate loads into independent variables and introducing the access path attenuation coefficient, the application overcomes the long-standing "negligible bias" in the field, significantly improves the frequency prediction accuracy under asymmetric loading, and simultaneously realizes a significant reduction in the amplitude imbalance degree and a several-fold improvement in the debugging efficiency.

Description

Technical Field

[0001] This invention belongs to the field of ion trap radio frequency system technology, specifically relating to a method for predicting the operating frequency, calibrating parameters, and adjusting the amplitude balance of a segmented linear Paul trap dual-output spiral resonator, belonging to the field of resonator design and radio frequency circuit debugging technology. Background Technology

[0002] Piecewise linear Paul traps are core devices for precision spectral measurements, quantum computing, and cold chemistry experiments, requiring the application of dual-path anti-phase radio frequency potentials in the radial direction to trap ions. Helical resonators are widely used to generate such high-amplitude radio frequency signals due to their compact structure, high voltage gain, good frequency selectivity, and small self-distributed capacitance, with typical operating frequencies covering the 1-50MHz band.

[0003] The classic design theory of spiral resonators was established by Macalpine and Schildknecht in 1959, which equates the resonator to the inductance of a secondary coil. With distributed capacitance This forms a resonator. Based on this, the engineering community has developed a universal lumped-parameter equivalent circuit model, which represents the resonator as a secondary coil inductance. Distributed capacitance and single load capacitor The resonant frequency of the parallel resonant circuit is given by the following formula:

[0004] (1)

[0005] For helical resonators with dual outputs, current technology generally combines the two load capacitors into a single parameter. Substitute into the above formula.

[0006] In engineering practice, amplitude balancing of dual-output spiral resonators often lacks systematic theoretical guidance. Conventional methods include: connecting variable capacitors in parallel at both outputs and trial-and-error by repeatedly sweeping frequencies to observe amplitude changes; or connecting an attenuation network in series at the output with the higher amplitude to passively reduce its output. These methods all rely on experience, have long adjustment cycles, and make it impossible to predict the direction and magnitude of the adjustment.

[0007] Research has revealed the following long-standing technical biases in resonator modeling and design, which are the root causes of the failure of existing models:

[0008] Bias 1: The belief that two loads can be combined into a single parameter for processing.

[0009] Traditional models implicitly assume that the two load paths are identical or can be equivalently combined. However, in actual ion trap systems, the two paths' directional electrode structures, feedthrough lengths, and solder joint impedances objectively differ, leading to variations in the capacitance of the two substrate load paths. and They are not equal. The traditional model of merging two loads completely fails in asymmetric loading scenarios.

[0010] Bias 2 (Core Bias): The assumption that the effective value of an external capacitor connected to the system via the access path is consistent with the actual measured value.

[0011] It is generally believed in the field that after the external capacitor is connected to the ion trap system through BNC cable, vacuum feedthrough and AC / DC coupling circuit, its effective value is basically consistent with the actual measured value, and the deviation is usually less than 5%. The influence of the distributed parameters of the access path is a second-order small quantity and can be ignored (referred to as "negligible bias").

[0012] This bias stems from design experience with low-frequency circuits (kHz and below), where the distributed parameter effects of cables and coupling circuits are indeed negligible. Those skilled in the art habitually extrapolate this experience to the MHz band without conducting systematic experimental verification. A search of existing literature on ion trap helical resonator design revealed no specific research on the interaction effect between the DC blocking inductor and the external capacitor in AC / DC coupling circuits.

[0013] Bias 3: The view that amplitude imbalance is mainly due to load mismatch rather than differences in base capacitance.

[0014] Intuitively, existing technology suggests that amplitude imbalance can be compensated for by adjusting the external load. However, experiments in this invention demonstrate that the imbalance remains essentially unchanged when both circuits are simultaneously loaded with the same capacitor, indicating that the root cause lies in the inherent difference in the base capacitor, rather than the external load.

[0015] The following system experiments reveal the aforementioned key deficiencies of the existing technology, and the data comparison is as follows:

[0016] Defect 1: Unable to describe dual-path independent loading.

[0017] Experiments show that when a 100pF capacitor is applied only to port 2 of the dual-output circuit, the resonant frequency predicted by the traditional model is 8.84MHz, which deviates significantly from the measured value of 11.10MHz, with a deviation as high as -20.38%. This means that the traditional model has essentially lost its engineering reference value in asymmetric loading scenarios.

[0018] Defect 2 (direct consequence of bias 2): Ignoring access path attenuation leads to serious inaccuracies in frequency prediction.

[0019] Comparative experiments revealed that when the external capacitor is fully connected to the ion trap system via BNC cable, vacuum feedthrough and AC / DC coupling circuit, its effective value in the 10-12MHz frequency band is only about 22.3% of the actual measured value (i.e., attenuation coefficient η=0.223), with an attenuation of up to 77.7%.

[0020] As a key control, when the external capacitor is directly connected to the resonator output (without passing through the AC / DC coupling circuit), the attenuation effect disappears, and the effective value is basically consistent with the actual measured value. This comparative experiment directly proves that the root cause of the attenuation effect lies in the impedance transformation effect between the AC / DC coupling circuit and the external capacitor, rather than the distributed parameters of the cable or feeder itself.

[0021] The attenuation rate of 77.7% far exceeds the common understanding in the field that "deviation <5%", completely overturning existing technological biases.

[0022] Defect 3: Lack of quantitative compensation methods for amplitude balancing.

[0023] Current technology relies solely on trial and error based on experience, making it impossible to predict the direction and magnitude of compensation. When the initial imbalance is 13.33%, the trial and error period is typically 2-5 days.

[0024] In summary, the fundamental problem with existing technologies lies in the flawed calculation method for the total load capacitance: dual-output loads are combined into a single parameter, and the effective value of the external capacitance is incorrectly equated to the actual measured value, resulting in a significant deviation between the calculated and actual total load capacitance. Since the total load capacitance is a core parameter determining the resonant frequency and output amplitude distribution of the resonator, its inaccurate calculation directly leads to a series of problems, including frequency prediction failure, Q-value evaluation deviation, and blind amplitude balance adjustment. Therefore, there is an urgent need for a method that can accurately calculate the total load capacitance of a dual-output spiral resonator and provide accurate fundamental parameters for subsequent frequency prediction and amplitude balance adjustment. Summary of the Invention

[0025] The purpose of this invention is to propose a method for calculating the total load capacitance of a dual-output spiral resonator and its application, in order to solve the following problems caused by the aforementioned technical biases in the prior art:

[0026] (1) Unable to describe the frequency response when dual-channel independent loading is applied;

[0027] (2) Ignoring the high-frequency attenuation effect of the access path leads to serious inaccuracies in frequency prediction;

[0028] (3) There is a lack of quantitative compensation methods for amplitude imbalance, and we can only rely on trial and error based on experience.

[0029] To achieve the above objectives, the technical solution of the present invention is as follows:

[0030] A method for calculating the total load capacitance of a dual-output spiral resonator includes the following steps:

[0031] Obtain the equivalent distributed capacitance of the resonator The equivalent capacitance of the two base loads at the operating frequency and and access path attenuation coefficient The access path attenuation coefficient Defined as the ratio of the effective value of the applied capacitor at the operating frequency to its actual measured value;

[0032] Calculate total load capacitance :

[0033]

[0034] In the formula, and These are the actual measured values ​​of the two external capacitors, respectively.

[0035] Preferably, the access path attenuation coefficient Calibrate using the following steps:

[0036] Step a1: Apply capacitors of the same capacitance value to both output terminals of the resonator simultaneously;

[0037] Step a2: Measure the resonant frequency after loading;

[0038] Step a3: Substitute into the dual-path decoupling high-frequency correction model for reverse calculation. :

[0039]

[0040] In the formula, The equivalent inductance of the secondary coil, The resonant frequency, This is the actual measured value of the external capacitor;

[0041] Step a4: For multiple groups of different Repeat steps a1-a3 to get the value. The average value is used as The calibration value.

[0042] Wherein, the access path attenuation coefficient It decreases as the operating frequency increases, with a typical value of 0.223 in the 10-12MHz band.

[0043] Preferably, after completing the access path attenuation coefficient calibration, an asymmetric loading model verification step is also performed:

[0044] The actual measured value is applied only to one of the output terminals of the resonator. The capacitance was measured, and the resonant frequency after loading was measured.

[0045] The currently calibrated access path attenuation coefficient Substitute the values ​​into the dual-path decoupling high-frequency correction model to calculate the predicted resonant frequency;

[0046] If the deviation between the measured value and the predicted value of the resonant frequency is greater than the preset threshold, the access path attenuation coefficient will be recalibrated.

[0047] Preferably, the access path attenuation coefficient During calibration, the external capacitor is selected from any one of the following: NP0 / C0G ceramic capacitor, X7R ceramic capacitor, or ordinary monolithic capacitor. Calibration results. Consistency proof It is independent of the type of external capacitor component, and is determined solely by the connection path.

[0048] A method for predicting the operating frequency of a dual-output spiral resonator, wherein the method uses the total load capacitance calculated by any of the methods described above, and substitutes it into a dual-channel decoupling high-frequency correction model to calculate the predicted resonant frequency value:

[0049]

[0050] In the formula, The equivalent inductance of the secondary coil, This is the resonant frequency.

[0051] A method for evaluating the loaded Q-value of a dual-output spiral resonator, wherein the loaded Q-value is calculated using the total load capacitance calculated by the method described in any one of claims 1-4, and the loaded Q-value is calculated according to the following formula. :

[0052]

[0053] in, The total loss resistance of the resonator is defined as follows: , The AC resistance of the secondary coil. For contact resistance, The equivalent series resistance of the load. The primary coil coupling impedance is calculated as follows; This is the equivalent inductance of the secondary coil.

[0054] Preferably, the total loss resistance of the resonator is determined by the following linear approximation formula:

[0055]

[0056] in, This is an engineering linear approximation of the total loss resistance of the resonator. and These are the empirically fitted parameters.

[0057] A method for amplitude balancing adjustment of a dual-output spiral resonator, wherein the amplitude balancing adjustment method is based on the equivalent capacitance of the two base loads at the operating frequency in the method described in any one of claims 1-4. and and access path attenuation coefficient Calculate the compensation capacitor value The voltage with the higher amplitude among the two base output voltages is used as the compensation port, and the actual measured value is connected to the compensation port. The compensation capacitor, or replacing the coaxial cable at the compensation port with a longer cable than the other one, with a length difference. , where k c is the capacitance coefficient of the coaxial line.

[0058] Preferably, the compensation capacitor is a high-frequency capacitor with NPO / COG dielectric.

[0059] Preferably, the method also includes a compensation verification step: after compensation, the output voltages V1' and V2' of the two base stations are measured, and the imbalance δ' after compensation is calculated. If δ' exceeds a preset threshold, compensation is performed again.

[0060] A dual-output spiral resonator system is characterized by using any of the above-mentioned methods for operating frequency prediction and using any of the above-mentioned amplitude balance adjustment methods for amplitude balance adjustment, wherein the operating frequency range of the system is 1-50MHz.

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] (1) It breaks through the “negligible bias” and the accuracy of frequency prediction leaps.

[0063] The revised model reduces the prediction error of the resonant frequency under asymmetric loading conditions from a maximum of 20.38% in the traditional model to less than 1.80%, with an average error of less than 0.6%. This improvement is far beyond what a person skilled in the art would reasonably expect.

[0064] (2) The access path attenuation effect was revealed quantitatively for the first time, which overturned the traditional understanding.

[0065] Comparative experiments show that after the external capacitor is fully connected to the ion trap system via BNC cable, vacuum feedthrough, and AC / DC coupling circuit, its effective value in the 10-12MHz frequency band is only about 22.3% of the actual measured value. =0.223), with an attenuation of 77.7%; in contrast, there is no attenuation when the external capacitor is directly connected to the resonator (without passing through the AC / DC coupling circuit). This comparative data directly refutes the long-standing technical bias in the field that "the influence of the access path is negligible".

[0066] (3) A non-trial-and-error amplitude balance adjustment method is provided.

[0067] Based on the modified model, the compensation capacitor value can be quantitatively predicted, reducing the imbalance from 13.33% to 0.34%, and shortening the debugging cycle from 2-5 days to 2-4 hours, a reduction of more than 90%.

[0068] (4) It is compatible with multiple compensation methods and can be implemented flexibly.

[0069] Lumped capacitance and distributed capacitance (coaxial line) have consistent mathematical descriptions under the modified model framework, allowing engineers to select the optimal solution based on available conditions.

[0070] (5) The calibration method is simple and does not require expensive equipment.

[0071] This invention requires only a signal generator and an oscilloscope to complete all calibrations, without the need for an impedance analyzer or network analyzer. Attached Figure Description

[0072] Figure 1 This is a circuit model diagram of an ion trap radio frequency system (Note: , , , The splitting is only used for graphical symmetry; in actual physics, these parameters are equivalent splits of the overall distribution parameters and do not affect the validity of the model.

[0073] Figure 2 Equivalent circuit of ion trap radio frequency system circuit model (Note: Figure 2 Will Figure 1 The "AC / DC coupling circuit and ion trap" within the red box in the diagram is equivalent to "resistor + capacitor", as shown in the figure. + and + );

[0074] Figure 3 For resonators and Calibration curve graph; the resonant frequency is measured by directly connecting the resonator to the load (a coaxial cable of a certain length); the horizontal axis represents the length of the connected coaxial cable. (cm), with the vertical axis representing the resonant frequency. (MHz), the scatter plot represents the experimental data, and the solid line represents the fitted curve of formula (1); where, , The capacitance of the coaxial line is expressed in pF / cm; fitting results. , , =1.06pF / cm;

[0075] Figure 4 This is a calibration curve of the access path attenuation coefficient η (symmetrical loading experiment, external capacitor through the complete access path—including AC / DC coupling circuit); the horizontal axis represents... (pF), the vertical axis is the frequency f (MHz), the scatter points are the experimental data, the solid line is the fitting curve of formula (2), and the fitting result is η=0.223;

[0076] Figure 5 A graph showing the change in Q value as a function of total load capacitance; the horizontal axis... (pF), vertical axis Q, scatter points are experimental data, solid line is the fitted curve of formula (8), fitting result =1.95Ω =1.6049×10 -4 Ω / pF;

[0077] Figure 6 This is a comparison chart of predictions and actual measurements using an asymmetric loading model; the horizontal axis... (pF), vertical axis frequency f (MHz, including measured value), corrected model prediction, and traditional model prediction, intuitively showing the accuracy advantage of the corrected model; the traditional model has a deviation of more than 20% at 100pF;

[0078] Figure 7 The degree of imbalance δ varies with A linear fit plot of the changes; through the formula The linear fitting results are a=0.00578, b=-0.10371, and the compensation point is 17.9pF.

[0079] Figure 8 This is an overall flowchart of the amplitude balance adjustment method for the dual-output spiral resonator of the present invention;

[0080] Figure 9 This is a schematic diagram of the overall architecture of the ion trap RF system. Note: During operation, a sinusoidal RF potential is generated by an arbitrary waveform generator, amplified by a power amplifier, and then amplified again by a resonator, achieving a peak-to-peak value of 500-1000V while maintaining a constant frequency. A static DC power supply generates an electrostatic potential (typically less than 5V), which is coupled to the RF potential via an AC / DC coupling circuit, ultimately providing the trapping potential for the ion trap. The loading capacitor is connected in parallel to the system via a BNC tee adapter when the resonator is connected to the AC / DC coupling circuit. Detailed Implementation

[0081] The following is in conjunction with the appendix Figure 1-9 The technical solution of the present invention will be described in detail below.

[0082] The technical solution adopted in this invention is:

[0083] First, a modified model for dual-path decoupling is established, retaining the two load capacitors as independent variables. An access path attenuation coefficient η is introduced into the model to quantitatively describe the attenuation effect of the external capacitance effective value of access paths such as BNC cables, AC / DC coupling circuits, and vacuum feedthroughs in the MHz frequency band.

[0084] Secondly, a complete parameter calibration process is proposed (no-load calibration → substrate calibration → symmetric loading calibration η → asymmetric loading verification), and all parameters are calibrated by frequency response measurement within the operating frequency band.

[0085] Finally, based on the calibrated correction model, the compensation capacitor value or cable length difference required for amplitude balance is quantitatively calculated, providing a non-trial-and-error debugging solution.

[0086] The technical solution is detailed below:

[0087] 1. Construction of the dual-path decoupling high-frequency correction model

[0088] This invention extends the traditional single-path lumped parameter model to a dual-path decoupled form, and the resonant frequency formula is:

[0089] (2)

[0090] The total load capacitance is:

[0091] (3)

[0092] The parameters in the formula are defined as follows:

[0093] — Equivalent inductance of secondary coil ( The dimensions of the coil and the number of turns are determined by its geometry.

[0094] — The equivalent distributed capacitance (pF) of the resonator is determined by the coil structure and the size of the shielding box;

[0095] , — The equivalent capacitance (pF) of the two substrate loads at the operating frequency, including the combined contribution of the ion trap electrode, vacuum feedthrough, BNC cable, DC-AC coupling circuit, etc.

[0096] , — The actual measured value (pF) of the two external capacitors, that is, the nominal capacitance measured at low frequency (usually 1kHz);

[0097] — Access path attenuation coefficient, dimensionless, defined as the ratio of the effective value of the external capacitor at the operating frequency to its actual measured value, 0 < η < 1.

[0098] The core innovation of this invention lies in:

[0099] (a) For the first time, the two load capacitors are decoupled into independent variables, enabling the model to distinguish "which one is loaded", breaking through the single variable limitation of the traditional model;

[0100] (b) Introduction of access path attenuation coefficient for the first time This quantitatively corrects the "negligible bias" that has long existed in this field.

[0101] 2. Physical meaning and experimental findings of the access path attenuation coefficient η

[0102] This invention discovered a key phenomenon in its experimental research:

[0103] When an external capacitor is connected to both outputs of the resonator via a BNC cable, vacuum feedthrough, and AC / DC coupling circuit, the effective value of this capacitor at the operating frequency is... Significantly lower than its actual measured value To quantitatively describe this phenomenon, the access path attenuation coefficient η is defined as:

[0104] (4)

[0105] in This is the effective value of the external capacitor at the operating frequency after passing through the complete access path (including BNC cable, vacuum feedthrough, and AC / DC coupling circuit).

[0106] To clarify the source of this attenuation effect, the inventors conducted a comparative experiment:

[0107] Control experiment: An external capacitor was directly connected to the output terminal of the resonator (without AC / DC coupling circuit), and its effect on the resonant frequency was measured. The results show that the actual measured value of the external capacitor is basically consistent with the measured effective value, and there is no significant attenuation phenomenon.

[0108] Complete system experiment: The same external capacitor was connected to the ion trap system (including BNC cable, vacuum feedthrough, AC / DC coupling circuit, and ion trap electrodes) via an AC / DC coupling circuit, and its effect on the resonant frequency was measured. The results show that the effective value of the external capacitor is only about 22.3% of the actual measured value. ≈0.223).

[0109] The above comparative experiments reveal an important fact: the root cause of the attenuation effect lies in the impedance transformation between the AC / DC coupling circuit and the external capacitor, rather than the distributed parameters of the BNC cable or the vacuum feedthrough itself. The AC / DC coupling circuit typically includes a DC-blocking inductor (passing DC, blocking AC) and a DC-blocking capacitor (passing AC, blocking DC). When an external capacitor is connected in parallel at the output, it forms an impedance transformation network with the inductor / capacitor components in the coupling circuit in the MHz band, causing the equivalent capacitance seen from the resonator output port to deviate from the actual measured value.

[0110] Another key finding of this invention is: The type of external capacitor is largely irrelevant. The inventors used NP0 / C0G, X7R, and ordinary monolithic capacitors in the same system and obtained consistent results. Value (see Example 3). This indicates It is a system path parameter—depending on the structure and operating frequency of the AC / DC coupling circuit, rather than the frequency characteristic parameter of the capacitor element itself.

[0111] It should be noted that the inventiveness of this invention does not rely on the complete theoretical derivation of the aforementioned physical mechanism. Regardless of the microscopic physical mechanism of the attenuation effect, this invention is the first to discover and quantitatively calibrate this attenuation effect through systematic experiments, and uses it to correct the resonator frequency prediction model and amplitude balance adjustment—this complete chain of "discovery-calibration-application" itself constitutes an inventive technical solution.

[0112] 3. Calibration method for access path attenuation coefficient η (symmetric loading method)

[0113] This is one of the key steps in this invention.

[0114] step:

[0115] (a1) Apply capacitors of the same capacitance value to both output terminals of the resonator simultaneously (i.e. = = , (This refers to the actual measured value of the applied capacitor).

[0116] (a2) Measure the resonant frequency after loading ;

[0117] (a3) Substitute into the modified model and reverse the calculation :

[0118] (5)

[0119] (a4) For multiple groups of different The values ​​were measured again, and each group was calculated by reverse calculation using equation (5). The value is taken as the arithmetic mean. The initial estimate is obtained; simultaneously, the overall least squares fit is performed on all data points using equation (2) as the objective function, and the fitting results are cross-validated with the average value. When the two are consistent (the deviation is less than 1%), the average value is taken as the result. The final calibration value.

[0120] Calibration conditions: , , It has been obtained in advance through no-load calibration and substrate calibration (the calibration method is described below).

[0121] 4. Lumped loss resistance model and Q-value evaluation

[0122] This invention introduces a total loss resistance R_total to describe the change in the loaded Q value:

[0123] (6)

[0124] in The AC resistance of the secondary coil. For contact resistance, The equivalent series resistance of the load. This is the reduced impedance for the primary coil coupling.

[0125] (7)

[0126] In engineering, a linear approximation is used, and the parameters are determined by experimental fitting:

[0127] (8)

[0128] 5. Amplitude Imbalance Analysis and Compensation Method Based on Modified Model

[0129] (1) Analysis method of the physical root cause of imbalance.

[0130] This invention, based on a modified model, reveals that when two circuits are simultaneously loaded with the same capacitor, the imbalance δ remains essentially constant (experiments show it to be stable at 10%-14%), proving that the root cause of the imbalance lies in the inherent difference between the two base load capacitors. This analytical method is another innovation of the present invention—shifting the imbalance problem from "external load adjustment" to "baseline difference compensation".

[0131] (2) Quantitative calculation method for compensation amount.

[0132] The unbalance δ is defined as:

[0133] (9)

[0134] Method 1 (calibration fitting method):

[0135] (a) Load multiple sets of different actual measured values ​​on the channel with higher amplitude (assuming port 2). The capacitance;

[0136] (b) Measure the imbalance of each group. ;

[0137] (c) Fitting - Linear relationship: ;

[0138] (d) Let δ=0, and solve for the value of the compensation capacitor: .

[0139] Method 2 (Direct Calculation Method):

[0140] If the specific values ​​of the two base capacitors are known and The required effective compensation capacitor is:

[0141] (10)

[0142] The corresponding external compensation capacitor value is:

[0143] (11)

[0144] (3) Compensation implementation plan.

[0145] Option 1 (lumped capacitance compensation): At the port with higher amplitude, use a BNC tee adapter to connect to an external terminal where the actual measured value is... The capacitor (preferably NP0 / C0G dielectric) is connected via the path Provides the required effective compensation after attenuation.

[0146] Option 2 (Distributed Capacitance Compensation – Coaxial Cable Method): Replace the BNC coaxial cable at the port with the higher amplitude with a longer cable than the other cable, utilizing the distributed capacitance of the coaxial cable for compensation. Required length difference:

[0147] (12)

[0148] in The capacitance factor (pF / cm) of the coaxial line used.

[0149] The advantage of Option 2 is that no additional components are required; compensation can be completed simply by adjusting the cable length.

[0150] Figure 8 The intermediate amplitude balance adjustment method includes the following steps:

[0151] S1—No-load calibration: Connect coaxial lines of different lengths across the two output terminals of the resonator, measure the resonant frequency, and fit the equivalent inductance of the secondary coil to obtain the calibration result. Distributed capacitance and coaxial line capacitance coefficient ;

[0152] S2—Substrate Calibration: Connect the ion trap system normally and measure the substrate resonant frequency f. base Inversely calculate the total load capacitance of the substrate. + Simultaneously measure the two output voltages V1 and V2, and calculate the initial unbalance δ0;

[0153] S3—Symmetrical Loading Calibration η: Two capacitors of the same capacitance are simultaneously applied to both circuits (the actual measured value of the applied capacitor is...). ), measure the resonant frequency after loading, and inversely deduce the attenuation coefficient η of the access path;

[0154] S4—Asymmetric Loading Model Validation: Actual measured values ​​are applied only to one of the paths. The capacitor is used to predict the resonant frequency using the calibrated correction model and compared with the measured value to verify whether the deviation is ≤2% (preset threshold). If not, return to S3 for recalibration.

[0155] S5—Unbalance Measurement and Compensation Calculation: Multiple capacitors are applied to the compensation port, and the corresponding unbalance δ is measured. The δ- value is then fitted. The curve is used to solve for the compensation capacitor value by setting δ=0. ;

[0156] S6—Compensation Implementation: Connect a compensation capacitor to the compensation port (Solution A), or replace the coaxial cable at the compensation port with a longer cable than the other cable, with a length difference Δl = η· (Option B);

[0157] S7—Compensation effect verification: Measure the two voltages V1' and V2' after compensation, and calculate the unbalance δ' after compensation. If δ'≤2%, the debugging is complete; otherwise, return to S5 to fine-tune the compensation amount.

[0158] Table 1 provides specific examples of the imbalance before and after compensation:

[0159] Table 1 Imbalance before and after compensation

[0160]

[0161] Example 1: No-load calibration of equivalent parameters of a spiral resonator

[0162] Experimental setup: The spiral resonator was wound with 2.0mm diameter copper wire, with a shielding layer diameter of 80mm and a height of 100mm. The secondary coil had a diameter of 39mm and 9 turns. Frequency response was measured using a signal generator (RIGOL DG4102) in conjunction with a digital oscilloscope (Tektronix TDS2024C), with a sweep frequency step of 100kHz. The ambient temperature was 25±2℃.

[0163] Calibration steps:

[0164] (1) Connect coaxial lines of different lengths (RG-58, 25-135cm) across the two output terminals of the resonator and measure the resonant frequency.

[0165] (2) With the length l (cm) of the coaxial line as the horizontal axis, f loaded Using the vertical axis, fit the data using formula (1) (see...) Figure 3 ).

[0166] Calibration result: L h =1.43μH, C e =5.466pF, k c =1.056pF / cm. Goodness of fit R²>0.999.

[0167] Example 2: Base Calibration and Initial Unbalance Measurement

[0168] step:

[0169] (1) Connect the ion trap system normally (including cables, vacuum feedthrough, and coupling circuit) without adding external capacitors.

[0170] (2) Measure the base resonance frequency .

[0171] (3) Calculate the total load capacitance of the substrate: + .

[0172] (4) Measure the two output voltages V1 and V2 and calculate δ0.

[0173] result: =11.82MHz, total substrate capacitance =121.32pF, V1=294V, V2=336V, δ0=13.33%.

[0174] Example 3: Calibration of Access Path Attenuation Coefficient η (Verification of Highlighting Technical Bias)

[0175] step:

[0176] (1) When two capacitors of the same capacity are applied simultaneously, the actual measured value of the applied capacitor is... .

[0177] (2) Measure each group η can be deduced from equation (5).

[0178] (3) To verify that η is independent of the capacitor type (disproving the possible explanation that "the frequency characteristics of the capacitor cause the deviation"), comparative experiments were conducted using NP0 / C0G, X7R, and ordinary monolithic capacitors. The capacitance values ​​were tested using a vector network analyzer at a frequency of 10 MHz.

[0179] result:

[0180]

[0181] η = 0.223 (mean), standard deviation 0.0017. NP0 / C0G capacitor η = 0.225, X7R capacitor η = 0.221, confirming that η is independent of capacitor type and determined solely by the connection path.

[0182] Compared with existing technological biases: Traditional models assume η=1 (i.e., effective value = actual measured value), with a bias of 77.7%. This invention completely disproves this bias through experiments.

[0183] Example 4: Verification of Asymmetric Loading Frequency Prediction (Comparison of Creative Effects)

[0184] Steps: Load only on port 2 (5-100pF), measurement Compared with the predictions of the modified model and the traditional model.

[0185] Key Results Table:

[0186]

[0187] Results Analysis (emphasizing creativity):

[0188] The traditional model's bias rapidly worsened from -1.50% to -20.38%—with a 100pF loading, the predicted value was only 79.6% of the measured value. This huge bias stems from a long-standing "negligible bias" in the field. The modified model controlled the bias to within 1.80%, validating the correctness of the η coefficient.

[0189] Demonstration of the non-obviousness of the technical effect: Under the influence of existing "negligible bias," those skilled in the art have no incentive to introduce an "attenuation coefficient" to correct the model. Even if someone is aware of the influence of cable distribution parameters, they cannot anticipate an attenuation as high as 77.7%, let alone think of using the symmetrical loading method to calibrate η and use it for amplitude balance compensation. Therefore, the steps of this invention are intrinsically related, and the whole constitutes a non-obvious technical solution.

[0190] Example 5: Amplitude Imbalance Analysis and Compensation

[0191] (a) Root cause analysis of imbalance (verifying the analytical capabilities of the model)

[0192] In the symmetrical loading experiment, δ stabilized between 10.68% and 13.33%, proving that the root cause was the difference in substrate capacitance rather than the external load.

[0193] (II) Compensation Point Prediction

[0194] Asymmetric loading experimental fitting: δ=0.00578 -0.10371 (R²=0.991), setting δ=0, we get =17.9pF.

[0195] (III) Implementation and Effects of Compensation

[0196]

[0197] All three schemes meet the engineering requirements of ion trap experiments for δ < 2%.

[0198] In summary, the technical effects of this invention are summarized in the table below:

[0199]

[0200] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for calculating the total load capacitance of a dual-output spiral resonator, characterized in that: Includes the following steps: Obtain the equivalent distributed capacitance of the resonator The equivalent capacitance of the two base loads at the operating frequency and and access path attenuation coefficient The access path attenuation coefficient Defined as the ratio of the effective value of the applied capacitor at the operating frequency to its actual measured value; Calculate total load capacitance : In the formula, and These are the actual measured values ​​of the two external capacitors, respectively.

2. The method for calculating the total load capacitance of a dual-output spiral resonator according to claim 1, characterized in that, The access path attenuation coefficient Calibrate using the following steps: Step a1: Apply capacitors of the same capacitance value to both output terminals of the resonator simultaneously; Step a2: Measure the resonant frequency after loading; Step a3: Substitute into the dual-path decoupling high-frequency correction model for reverse calculation. : In the formula, The equivalent inductance of the secondary coil, The resonant frequency, This is the actual measured value of the external capacitor; Step a4: For multiple groups of different Repeat steps a1-a3 to get the value. The average value is used as The calibration value.

3. The method for calculating the total load capacitance of a dual-output spiral resonator according to claim 2, characterized in that, After completing the calibration of the access path attenuation coefficient, the asymmetric loading model verification step is also performed: The actual measured value is applied only to one of the output terminals of the resonator. The capacitance was measured, and the resonant frequency after loading was measured. The currently calibrated access path attenuation coefficient Substitute the values ​​into the dual-path decoupling high-frequency correction model to calculate the predicted resonant frequency; If the deviation between the measured value and the predicted value of the resonant frequency is greater than the preset threshold, the access path attenuation coefficient will be recalibrated.

4. The method for calculating the total load capacitance of a dual-output spiral resonator according to claim 2, characterized in that, The access path attenuation coefficient In the calibration, the external capacitor is selected from any one of NP0 / C0G ceramic capacitors, X7R ceramic capacitors, or ordinary monolithic capacitors.

5. A method for predicting the operating frequency of a dual-output spiral resonator, characterized in that, The operating frequency prediction method uses the total load capacitance calculated by the method described in any one of claims 1-4, and substitutes it into the dual-path decoupling high-frequency correction model to calculate the predicted resonant frequency value: In the formula, The equivalent inductance of the secondary coil, This is the resonant frequency.

6. A method for evaluating the loaded Q-value of a dual-output spiral resonator, characterized in that, The loading Q-value evaluation method uses the total load capacitance calculated by the method described in any one of claims 1-4, and calculates the loading Q-value according to the following formula. : in, The total loss resistance of the resonator is defined as follows: , The AC resistance of the secondary coil. For contact resistance, The equivalent series resistance of the load. The primary coil coupling impedance is calculated as follows; This is the equivalent inductance of the secondary coil.

7. The method for evaluating the loaded Q value of a dual-output spiral resonator according to claim 6, characterized in that, The total loss resistance of the resonator is determined by the following linear approximation formula: in, This is an engineering linear approximation of the total loss resistance of the resonator. and These are the empirically fitted parameters.

8. A method for adjusting the amplitude balance of a dual-output spiral resonator, characterized in that, The amplitude balance adjustment method is based on the equivalent capacitance of the two base loads at the operating frequency in any one of claims 1-4. and and access path attenuation coefficient Calculate the compensation capacitor value ; The voltage with the higher amplitude among the two base output voltages is used as the compensation port, and the actual measured value is connected to the compensation port. The compensation capacitor, or replacing the coaxial cable at the compensation port with a longer cable than the other one, with a length difference. , where k c is the capacitance coefficient of the coaxial line.

9. The amplitude balance adjustment method for a dual-output spiral resonator according to claim 8, characterized in that, The compensation capacitor is selected as a high-frequency capacitor with NPO / C0G dielectric.

10. The amplitude balance adjustment method for a dual-output spiral resonator according to claim 8, characterized in that, It also includes a compensation verification step: after compensation, measure the output voltages V1' and V2' of the two base stations, calculate the imbalance δ' after compensation, and if δ' exceeds the preset threshold, perform compensation again.

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