An Optimal Design Method for Inductive Magnetic Sensors

Abstract

The present invention discloses an optimization design method for an inductive magnetic sensor. First, the quality, length, and target noise level of the design requirements are proposed, and then the noise of the inductive magnetic sensor is systematically analyzed. According to the quality factor, the quality of the magnetic core and the winding is allocated. Then, according to the aspect ratio m of the magnetic core and the initial magnetic permeability μ of the magnetic core material r , the magnetic core is optimized in design. Finally, the winding is optimized in design to obtain the optimal wire diameter #imgabs0# and the optimal number of coil turns n opt . Ultimately, the optimal design scheme of the inductive magnetic sensor in the theoretical case is obtained. This method deeply and systematically analyzes the noise of the inductive magnetic sensor, establishes a mathematical model from two perspectives of the sensor magnetic core design and the coil design, numerically calculates various parameters required for the design, and uses the calculation results to manufacture the inductive magnetic sensor. The calculation process of this optimization design method is simple, greatly shortening the development time and reducing the R & D cost, and having good practicability.

Description

Technical Field

[0001] The invention belongs to the technical field of inductive magnetic sensors, and in particular to the technical field of optimized design of inductive magnetic sensors. Background Art

[0002] Induction or search-coil magnetometers (IM) have the advantages of wide frequency range, simple physical structure and low cost. They are the most widely used sensors in magnetotelluric sounding.

[0003] Compared with the noise, the signal of the geomagnetic field is mainly distributed in the range of 10 -4 ~10 6 In the Hz frequency band, the geomagnetic field signal shows an attenuation trend between the frequency of 0.0001Hz and 1kHz, and the intensity decreases from 1000nT to below 0.01nT, with an attenuation amplitude of more than five orders of magnitude; when the frequency is around 0.5Hz, 3Hz and 1000Hz, the geomagnetic field signal has a minimum value; when the frequency is in the very low frequency band, due to the existence of Schumann resonance, the magnetic field intensity value increases. During the development process, it is necessary to strictly control the noise level of the inductive magnetic sensor so that the background noise of the sensor is much lower than the geomagnetic field signal in the full frequency band, so as to receive effective signals from the geomagnetic field.

[0004] The noise of inductive magnetic field sensors mainly comes from coils and preamplifiers. Generally speaking, the higher the magnetic permeability of the magnetic core, the larger the aspect ratio, and the more turns of the coil, the higher the sensitivity of the inductive magnetic sensor, and the lower the noise level. However, considering the portability of construction, the durability of the sensor, and the need for easy maintenance, inductive sensors that are too long or have too large a cross-sectional area or too many turns of winding do not meet actual needs. In addition, the development of inductive magnetic sensors requires repeated trial production processes such as design, production, and testing, and there are problems with long R&D cycles and low R&D efficiency.

[0005] Based on the above description, an optimization design method for inductive magnetic sensors is urgently needed to solve the problem that the inductive magnetic sensor research and development design process requires repeated design, production, and testing, and the research and development cycle is long. Summary of the invention

[0006] The purpose of the present invention is to provide an optimization design method for an inductive magnetic sensor, through which the optimal solution under given noise conditions can be obtained according to numerical calculations, thereby greatly reducing the number and time of trial production of the inductive magnetic sensor.

[0007] In order to solve the above technical problems, the specific technical solution of an inductive magnetic sensor optimization design method of the present invention is as follows:

[0008] An inductive magnetic sensor optimization design method comprises the following steps:

[0009] S1. Given design conditions: length, mass and target frequency noise level;

[0010] S2, perform a systematic analysis of the inductive magnetic sensor noise;

[0011] S3, allocating the mass of the core and the conductor according to the mass factor;

[0012] S4, the aspect ratio m of the inductive magnetic sensor core and the initial magnetic permeability μ of the material r Carry out optimization design;

[0013] S5. Optimize the winding design of the inductive magnetic sensor to obtain the optimal wire diameter and the optimal number of coil winding turns n opt ;

[0014] S6, verify whether all target conditions are met: if so, execute S7; if not, re-execute S4 and S5;

[0015] S7. Obtain the optimal design scheme of the inductive magnetic sensor under theoretical conditions.

[0016] Furthermore, the system analysis of the inductive magnetic field sensor noise described in S2 is as follows:

[0017] The equivalent magnetic noise of the inductive magnetic field sensor is mainly composed of the thermal noise of the coil resistance and the voltage noise and current noise of the preamplifier. The total equivalent magnetic field noise level is:

[0018]

[0019] in: is the equivalent magnetic field noise of the coil resistance thermal noise, is the equivalent magnetic field noise of the preamplifier voltage noise, is the equivalent magnetic field noise of the preamplifier current noise.

[0020] Furthermore, the equivalent magnetic field noise of the coil resistance thermal noise is for:

[0021]

[0022] The equivalent magnetic field noise of the preamplifier voltage noise for:

[0023]

[0024] The equivalent magnetic field noise of the preamplifier current noise for:

[0025]

[0026] Furthermore, the aspect ratio m of the magnetic core and the initial magnetic permeability μ of the material in S4 are r The optimization process is:

[0027] The total noise NL of the inductive magnetic sensor is:

[0028]

[0029] in

[0030]

[0031] Take the second-order derivative of m, NL″=0, and get the solution m opt , get the optimized core aspect ratio,

[0032] For μ r Find the first-order derivative, NL′=0, and get the solution μ ropt , and obtain the optimized initial magnetic permeability of the material.

[0033] Further, the step S3 allocates the core and wire quality according to the quality factor and the step S5 allocates the optimal wire diameter according to the quality factor. The calculation method is:

[0034] Define a quality factor q, the value of q is equal to the coil mass W w and the core mass W C The ratio of

[0035] The total noise NL of an inductive magnetic sensor is expressed in terms of the quality factor q:

[0036]

[0037] Where W w is the mass of the coil, f is the frequency of the induced magnetic field, and E is a constant related to the magnetic core and the coil;

[0038] Take the first-order derivative of q, set NL′=0, and the solution q opt , which is the best quality factor;

[0039] The total noise NL of the inductive magnetic sensor is expressed as w It is expressed as:

[0040]

[0041] Right w Find the second-order derivative, set NL″=0, and get the solution At this time When the wire diameter increases, the effect on the noise level becomes smaller, and the optimal wire diameter is obtained.

[0042] Furthermore, the optimal number of coil winding turns n in step S5 is opt The calculation method is:

[0043] According to S3, the core diameter, length and material can be determined, and the core mass W can be determined C , calculate the optimal coil quality

[0044]

[0045] According to the best coil quality and optimum wire diameter Calculate the optimal number of coil winding turns n opt .

[0046] Furthermore, the verification process of step S6 is:

[0047] Substitute the optimized parameters into the target frequency calculation to verify the optimized core diameter, length and material, and the best wire diameter under the conditions of meeting the target quality and length. and the optimal number of coil winding turns n opt Whether they can meet the noise level requirements of different targets at the same frequency and obtain the final optimization result.

[0048] The inductive magnetic sensor optimization design method of the present invention has the following advantages:

[0049] This method conducts an in-depth and systematic analysis of the noise of the inductive magnetic sensor. After giving the required target sensor quality and noise level, it establishes a mathematical model from the two perspectives of sensor core design and coil design, performs numerical calculations on various required parameters, and uses the calculation results to make an inductive magnetic sensor. The calculation process of this optimization design method is simple, greatly shortens the development time, reduces the R&D cost, and has good practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic diagram of the structure of the inductive magnetic sensor model of the present invention;

[0051] Figure 2 It is a schematic diagram of the inductive magnetic sensor circuit of the present invention;

[0052] Figure 3 This is a noise distribution diagram of the inductive magnetic sensor of the present invention;

[0053] Figure 4 The noise curve of the inductive magnetic sensor of the present invention changes with the aspect ratio;

[0054] Figure 5 The noise of the inductive magnetic sensor of the present invention changes with the initial magnetic permeability;

[0055] Figure 6 is the quality factor of the inductive magnetic sensor coil of the present invention;

[0056] Figure 7 The best quality of the inductive magnetic sensor coil of the present invention;

[0057] Figure 8 is the wire diameter of the inductive magnetic sensor coil of the present invention;

[0058] Fig. 9 is the number of turns of the inductive magnetic sensor coil winding of the present invention;

[0059] Fig.10 A comparison chart of theoretical values ​​and measured values ​​of the optimization design method of the present invention;

[0060] Fig.11 The present invention is an optimization design method flow chart. DETAILED DESCRIPTION

[0061] In order to better understand the method and steps of the present invention, the following further describes in detail an inductive magnetic sensor optimization design method of the present invention in conjunction with the accompanying drawings.

[0062] The theoretical basis and derivation process of an inductive magnetic sensor optimization design method of the present invention are as follows:

[0063] The schematic diagram of the inductive magnetic sensor model structure of the present invention is as follows: Figure 1 shown.

[0064] The schematic diagram of the inductive magnetic sensor circuit of the present invention is as follows: Figure 2 shown.

[0065] First, determine the noise expression:

[0066] According to Ferrari's law of electromagnetic induction, the expression of the induced voltage V is:

[0067]

[0068] Where n is the number of turns, S is the cross-sectional area, μ app is the apparent magnetic permeability of the core, B is the magnetic induction intensity, and the negative sign indicates that the direction of the induced electromotive force is along the direction that hinders the change of magnetic flux.

[0069] This formula can be rewritten in the frequency domain as:

[0070] V=-jωμ app nB

[0071] Among them, ω=2πf.

[0072] The voltage sensitivity σ can be expressed as:

[0073]

[0074] Then the thermal noise e r The expression is:

[0075]

[0076] Where T is the Kelvin temperature, R is the resistance of the coil, and f is the frequency of the induced magnetic field.

[0077] The signal resolution of the sensor is Then the equivalent magnetic field noise level formula of the induction coil resistance thermal noise is expressed as:

[0078]

[0079] In the formula, k b is the Boltzmann constant, which is 1.38×10 -23 J / K.

[0080] The expression of R is:

[0081]

[0082] Where, d i is the inner diameter of the coil, d w is the wire diameter.

[0083] Then the equivalent magnetic field noise level formula of the induction coil resistance thermal noise is expressed as:

[0084]

[0085] The equivalent magnetic field noise of the voltage noise at the preamplifier input and the equivalent magnetic field noise of the current noise are:

[0086]

[0087] Where L is the coil inductance, C is the coil distributed capacitance, e n is the voltage noise at the preamplifier input, i n is the current noise at the preamplifier input. For a given preamplifier circuit, e n and i n is a known value.

[0088] From this, the total equivalent magnetic field noise level of the coil can be obtained as follows:

[0089]

[0090] The influence of each part of noise on the total noise is as follows Figure 3 shown.

[0091] First, optimize the design of the magnetic core. The magnetic core is the main component of the inductive sensor. However, due to the demagnetization effect of the magnetic field, the apparent magnetic permeability of the magnetic core is much lower than the relative magnetic permeability of the core material and is seriously affected by the geometric shape of the magnetic core.

[0092] The attenuation law of magnetic permeability is mathematically analyzed, and the aspect ratio of the magnetic core is defined as m, its length is l, its diameter is d, and the initial magnetic permeability of the magnetic core is μ r , the apparent magnetic permeability of the core is μ app , then m=l / d.

[0093] Demagnetization coefficient of the core N r It is only related to the aspect ratio m of the core, which is:

[0094]

[0095] Apparent magnetic permeability μ app for:

[0096]

[0097] The total noise of the sensor can be expressed as:

[0098]

[0099] in

[0100]

[0101] Use this formula to calculate the effect of the change in the aspect ratio of the core on the total noise of the sensor, then find the second-order derivative of m and set the second-order derivative equal to zero to obtain the corresponding solution:

[0102] m opt =40:

[0103] That is, when the aspect ratio m>40, the second-order derivative changes from positive to negative, the rate at which the noise level changes with the aspect ratio decreases, and the effect of increasing the aspect ratio on improving sensor noise decreases, such as Figure 4 shown.

[0104] Then calculate the effect of the change in core permeability on the total sensor noise. r Find the first-order derivative and set NL′=0 to obtain the solution μ ropt =10 5 H / m. When μ r >10 5H / m, the noise intensity does not change with the change of magnetic permeability. At this time, the noise intensity is much smaller than the geomagnetic field intensity, meeting the requirements, such as Figure 5 shown.

[0105] Finally, optimize the coil design:

[0106] The coil optimization design is related to the magnetic core. After the magnetic core is optimized, the mass of the magnetic core can be calculated. In order to simplify the calculation, a quality factor q is defined, and the value of q is equal to the ratio of the coil mass to the magnetic core mass. If q has an optimal solution, it proves that the best quality that can meet the noise requirements exists.

[0107] Generally speaking, the coil mass W w The expression is:

[0108]

[0109] In the formula, l m is the average length of each coil turn, δ w is the average density of copper wire, d w is the diameter of the enameled wire, γ d is the filling factor, d w is the copper wire diameter.

[0110] Core mass W C and total mass W S The expression is:

[0111]

[0112] W S =W W +W C

[0113] In the formula, δ c is the average density of the magnetic core, resistance According to the determined core diameter, length and material, the core mass W C It is a fixed value.

[0114] Geometric parameter α = d i / d,z=d o / d i , sensor winding ratio β = l w / l, the winding filling factor is γ w .

[0115] Then the number of turns n is expressed by geometric parameters as:

[0116]

[0117] The wire diameter is then:

[0118]

[0119] Coil mass W w for:

[0120]

[0121] Then the expression of quality factor q is:

[0122]

[0123] make but:

[0124] z 2 =1+qE

[0125] The noise can be expressed by the quality factor as:

[0126]

[0127] Among them, the quality factor q has an optimal value, which makes the total noise of the magnetic sensor minimum when the quality is the same. Taking the derivative of q and setting NL′=0, the minimum value obtained is the optimal quality factor q opt ,like Figure 6 shown.

[0128] At this time, the mass of the magnetic core is fixed, and the quality factor q = q opt , the mass of the coil has a unique value like Figure 7 As shown. Therefore, the optimal total mass value of the inductive magnetic sensor that meets the noise requirements is obtained.

[0129]

[0130] The coil quality mainly depends on the wire diameter and the number of winding turns. When the wire diameter and the number of winding turns are optimized, the signal-to-noise ratio of the inductive magnetic sensor is maximized. The increase in the wire diameter reduces the noise level of the entire coil to a certain extent, but at the same time increases the winding ratio of the coil and increases the mass of the coil. Therefore, a reasonable wire diameter needs to be selected during the design process. w Substituting into the noise formula, we get NL with respect to d w The expression is:

[0131]

[0132] Right w Find the second-order derivative, NL″=0, and we get When the wire diameter is larger than The noise reduction is no longer significant. is the optimal wire diameter, such as Figure 8 shown.

[0133] According to the best coil quality and optimum wire diameter Calculate the optimal number of coil winding turns n opt ,like Fig. 9 shown.

[0134] Substitute the optimization parameters into the calculation and verify the optimized core diameter, length and material, and the optimal wire diameter while meeting the target length and quality. and the optimal number of coil winding turns n opt Whether it can meet the noise level requirements at different target frequencies and whether the noise level in the entire frequency range is much lower than the geomagnetic signal, the final optimization result can be obtained.

[0135] The feasibility of the method will be verified using a specific case.

[0136] Design example target requirements: frequency range: 1Hz ~ 100kHz, total mass less than 2.5kg, length less than 750mm, noise:

[0137] A 1Hz-100kHz inductive magnetic sensor coil is wound according to the calculation result of the optimization formula, an inductive magnetic sensor is obtained by winding the coil according to the plan, and the obtained inductive magnetic sensor is measured.

[0138] Among them, the design parameters and measurement results are shown in the following table:

[0139]

[0140]

[0141] The actual total mass of the sensor, housing and potting glue is 2.1kg, and the length is 720mm, which meets the length and mass requirements; the measured noise power spectrum density is as follows: Fig.10 As shown, they are all less than the target parameters and meet the design requirements. Around 1Hz, the measured noise power spectrum density increases due to the influence of the 1 / f noise of the preamplifier circuit. When f>1kHz, the core loss causes the measured noise power spectrum density to be greater than the theoretical calculated value. In addition, the power spectrum density of the measured noise in the entire frequency range is lower than the power spectrum density of the geomagnetic field signal, proving that the results of the optimal design fully meet the requirements.

[0142] According to the above derivation and verification, if Fig.11As shown, the present invention provides an inductive magnetic sensor optimization design method, comprising the following steps:

[0143] S1. Given the design target conditions: length, mass and noise level;

[0144] S2, perform a systematic analysis of the inductive magnetic sensor noise;

[0145] S3, allocating the mass of the core and the conductor according to the mass factor;

[0146] S4, the aspect ratio m of the inductive magnetic sensor core and the initial magnetic permeability μ of the material r Carry out optimization design;

[0147] S5. Optimize the winding design of the inductive magnetic sensor to obtain the optimal wire diameter and the optimal number of coil winding turns n opt ;

[0148] S6, verify whether all target conditions are met: if so, execute S7; if not, re-execute S4 and S5;

[0149] S7. Obtain the optimal design scheme of the inductive magnetic sensor under theoretical conditions.

[0150] It is to be understood that, as known to those skilled in the art, various changes or equivalent substitutions may be made to the method without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, the method may be modified to adapt to specific circumstances without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of the present application are within the scope of protection of the present invention.

Claims

1. An optimization design method for an inductive magnetic sensor, characterized in that: The following steps are involved: S1. Given design conditions: length, mass and target frequency noise level; S2, perform a systematic analysis of the inductive magnetic sensor noise; S3, allocating the mass of the core and the conductor according to the mass factor; S4, the aspect ratio m of the inductive magnetic sensor core and the initial magnetic permeability μ of the material r Carry out optimization design, the optimization process is: The total noise NL of the inductive magnetic sensor is: in Where, ω = 2πf; n is the number of turns; S is the cross-sectional area; k b is the Boltzmann constant; T is the Kelvin temperature; d i is the inner diameter of the coil; d w is the wire diameter; e n is the voltage noise at the preamplifier input; i n is the current noise at the input of the preamplifier; R is the resistance of the coil; C is the distributed capacitance of the coil; L is the inductance of the coil; f is the frequency of the induced magnetic field; Taking the second-order derivative of m, NL″=0, we get the aspect ratio m of the core. For μ r Find the first-order derivative, NL′=0, and get the initial magnetic permeability μ of the material r ; S5. Optimize the winding design of the inductive magnetic sensor to obtain the optimal wire diameter and the optimal number of coil winding turns n opt ; Step S3 allocates the core and wire mass according to the quality factor and Step S5 allocates the optimal wire diameter The calculation method is: Define a quality factor q, the value of q is equal to the coil mass W w and the core mass W C The ratio of The total noise NL of an inductive magnetic sensor is expressed in terms of the quality factor q as: Where W w is the mass of the coil, f is the frequency of the induced magnetic field, and E is a constant related to the magnetic core and the coil; Take the first-order derivative of q and set NL' = 0. The minimum value obtained is the optimal quality factor q opt ; The total noise NL of the inductive magnetic sensor is expressed as: In the formula, δ c is the average density of the magnetic core; Take the second-order derivative of dw and set NL" = 0 to obtain the solution when When the wire diameter increases, the effect on the noise level becomes smaller, and the optimal wire diameter is obtained. The optimal coil winding turns n opt The calculation method is: According to S3, the core diameter, length and material can be determined, and the core mass W can be determined. C , Calculating the optimum coil quality According to the best coil quality and optimum wire diameter Calculate the optimal number of coil winding turns n opt ; S6, verify whether all target conditions are met: if so, execute S7; if not, re-execute S4 and S5; S7. Obtain the optimal design scheme of the inductive magnetic sensor under theoretical conditions.

2. The method for optimizing the design of an inductive magnetic sensor according to claim 1, characterized in that: S2 describes a systematic analysis of the inductive magnetic sensor noise as follows: The equivalent magnetic noise of the inductive magnetic field sensor is mainly composed of the thermal noise of the coil resistance and the voltage noise and current noise of the preamplifier. The total equivalent magnetic field noise level is: in: is the equivalent magnetic field noise of the coil resistance thermal noise, is the equivalent magnetic field noise of the preamplifier voltage noise, is the equivalent magnetic field noise of the preamplifier current noise.

3. The method for optimizing the design of an inductive magnetic sensor according to claim 2, characterized in that: The equivalent magnetic field noise of the coil resistance thermal noise for: Where μ app is the apparent magnetic permeability of the core; The equivalent magnetic field noise of the preamplifier voltage noise for: The equivalent magnetic field noise of the preamplifier current noise for:

4. The method for optimizing the design of an inductive magnetic sensor according to claim 1, characterized in that: The verification process of step S6 is: Substitute the optimized parameters into the target frequency calculation to verify the optimized core diameter, length and material, and the best wire diameter under the conditions of meeting the target quality and length. and the optimal number of coil winding turns n opt Whether they can meet the noise level requirements of different targets at the same frequency and obtain the final optimization result.

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