CN113933591A - Method for measuring lumped electrical parameters of solenoid micro-coil - Google Patents
Method for measuring lumped electrical parameters of solenoid micro-coil Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R27/00—Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
- G01R27/02—Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R27/00—Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
- G01R27/02—Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
- G01R27/26—Measuring inductance or capacitance; Measuring quality factor, e.g. by using the resonance method; Measuring loss factor; Measuring dielectric constants ; Measuring impedance or related variables
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R27/00—Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
- G01R27/02—Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
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Abstract
The invention discloses a method for measuring lumped electrical parameters of a solenoid micro-coil, and belongs to the technical field of microwave measurement. Respectively manufacturing a clamp of the piece to be tested and a TRL embedded calibration piece, and measuring S parameters of the piece to be tested of the solenoid micro-coil and the embedded calibration piece by using a network analyzer; performing data processing on the measured S parameter by using a TRL de-embedding algorithm to obtain the S parameter of the solenoid micro-coil; obtaining the Z parameter of the solenoid micro-coil according to the conversion relation between the S parameter and the Z parameter; and establishing a lumped equivalent circuit model of the solenoid micro-coil, analyzing to obtain a mathematical relation between lumped electrical parameters and Z parameters of the solenoid micro-coil, and performing data processing on the Z parameters of the solenoid micro-coil by utilizing nonlinear least square fitting to obtain an estimated value and precision of the lumped electrical parameters of the solenoid micro-coil. The method can eliminate the error caused by the measuring clamp and improve the measuring precision of the lumped electrical parameter of the solenoid micro coil.
Description
Technical Field
The invention belongs to the technical field of microwave measurement, and particularly relates to a method for measuring lumped electrical parameters of a solenoid micro-coil.
Background
The implantable micro-device is injected into a deeper position in a body in a minimally invasive surgery mode, has good targeting property, and has important practical significance for accurate diagnosis and treatment of diseases. However, because the size is small, generally 1-2 mm, a rechargeable or disposable battery cannot be used as a power supply, and the midfield wireless energy transfer technology provides an effective way for energy supply of the deep-implanted micro device.
The deep implantation micro device adopting the midfield wireless energy transmission technology uses the solenoid micro coil as an in-vivo energy receiving coil, measures lumped electrical parameters (resistance, inductance, capacitance, resonant frequency and quality factor) of the solenoid micro coil, and becomes a premise and a basis for reasonably designing an in-vivo energy receiving circuit and improving the percutaneous wireless energy transmission efficiency.
The geometric dimension of the solenoid micro-coil is generally 1-2 mm, and the resonant frequency is generally in the GHz level. For a general low-frequency solenoid coil, an LCR tester or an impedance analyzer can be used for measurement, but for a solenoid micro-coil with the resonance frequency in the GHz level, the LCR tester or the impedance analyzer cannot meet the higher frequency requirement; although the vector network analyzer can provide GHz measuring frequency, the measuring error introduced by the contact resistance, the inductance, the capacitance and the like of the measuring clamp is not negligible, and the requirement of the precision of the solenoid micro-coil lumped electrical parameter measurement cannot be met.
The research group of the German Flieberg university provides a wireless induction mode for non-contact measurement of lumped electrical parameters (resistance, inductance and capacitance) of a small coil, which is different from the traditional contact type measurement method, a larger solenoid coil is adopted as a magnetic field coupling probe, an impedance analyzer is adopted to measure the impedance parameter of the small coil, and an analytical model of inductive coupling is utilized to calculate the lumped electrical parameter of the small coil, so that the complicated operation process of contact detection of the small coil is omitted, and the contact resistance, the additional inductance and the parasitic capacitance introduced by clamp connection in the measurement process are avoided. However, because coupling capacitance exists between the magnetic field coupling probe and the small coil and is related to frequency, the influence caused by the coupling capacitance cannot be ignored during high-frequency measurement, and meanwhile, due to the uneven magnetic field generated by excessively high frequency, the magnetic field probe and the small coil to be measured have nonlinear coupling, so that the measurement error is larger when the frequency is higher, and the method is not suitable for measuring lumped electrical parameters of the GHz solenoid micro-coil.
Disclosure of Invention
In this summary, concepts in a simplified form are introduced that are further described in the detailed description. This summary of the invention is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.
Aiming at the defects of the prior art, the invention aims to provide a method for measuring lumped electrical parameters of a solenoid micro-coil, and aims to solve the problem that the lumped electrical parameters of the solenoid micro-coil cannot be accurately measured.
In order to achieve the purpose, the invention provides a method for measuring lumped electric parameters of a solenoid micro-coil, which adopts a microwave network analysis technology and a TRL de-embedding method, measures scattering parameters (S parameters) of the solenoid micro-coil by using a vector network analyzer and a de-embedding calibration part, calculates Z parameters of the solenoid micro-coil by using the corresponding relation of the S parameters and impedance parameters (Z parameters), analyzes and obtains a functional relation formula of the Z parameters and the lumped electric parameters of the solenoid micro-coil according to a lumped equivalent circuit model of the solenoid micro-coil, and further obtains an estimated value and the precision of the lumped electric parameters of the solenoid micro-coil by using a nonlinear least square fitting method. The method comprises the following steps:
the clamp is designed according to the size of the solenoid micro-coil to be tested, and comprises a radio frequency connector, a printed circuit board, two sections of microstrip lines with the same length and a base. Welding the solenoid micro-coil to be tested between two sections of microstrip lines of the clamp to form a solenoid micro-coil to be tested; designing and manufacturing a calibration piece according to the structural size of the piece to be tested of the solenoid coil, wherein the calibration piece comprises a direct calibration piece, a reflection calibration piece and a transmission line calibration piece;
respectively measuring S parameter matrixes of a solenoid micro-coil to-be-measured piece and a calibration piece;
calculating an S parameter matrix of the solenoid micro coil to be measured according to the S parameter matrices of the solenoid micro coil to be measured and the calibration piece by using a TRL de-embedding method, obtaining the resonance frequency and the quality factor of the solenoid micro coil, and obtaining a Z parameter matrix of the solenoid micro coil by using the corresponding relation of the S parameter and the Z parameter;
and obtaining the equivalent series resistance, the equivalent inductance and the equivalent parallel capacitance of the solenoid micro-coil by utilizing a nonlinear least square fitting method according to the Z parameter matrix.
Preferably, the straight-through calibration piece comprises a section of microstrip line, the length of the straight-through calibration piece is the same as the sum of the lengths of the two sections of microstrip lines of the solenoid micro-coil piece to be tested, the transmission coefficient of the straight-through calibration piece is 1, and the reflection coefficient of the straight-through calibration piece is 0. The reflection calibration piece comprises two sections of microstrip lines, the lengths of the two sections of microstrip lines are the same as the length of the microstrip line of the solenoid micro-coil piece to be tested, and the transmission coefficient and the reflection coefficient of the reflection calibration piece are respectively 0 and-1. The transmission line calibration piece comprises a section of microstrip line, the length of the microstrip line is larger than that of the solenoid micro-coil piece to be tested, and the transmission phase delay of the transmission line calibration piece relative to the straight-through calibration piece is between 20 degrees and 160 degrees.
Further, the S parameter matrix of the solenoid micro-coil under test:
wherein, s'11、s′21、s′22、s′12Measured values of an S-parameter matrix for a solenoid micro-coil test piece, e30Is a positive leakage error, e03Is a negative leakage error, e11Is a positive match error, e22Is a negative match error, e10e01Is the forward reflection frequency response error, e23e32Is a negative reflection frequency response error, e10e32Is the forward transmission frequency response error, e23e01Is a negative transmission frequency response error, e00Is a forward direction error, e33Is a negative direction error.
Further, the air conditioner is provided with a fan,
e30＝R21
e03＝R12
wherein, T11、T21、T22、T12Respectively representing measured values, R, of a matrix of S-parameters of said pass-through calibration member11、R21、R22、R12Respectively representing the measured values of the S-parameter matrix of the reflective calibration member, L11、L21、L22、L12Respectively representing the measured values of the S parameter matrix of the transmission line calibration piece.
Preferably, the microstrip line is metal.
Through the technical scheme, compared with the prior art, the invention can obtain the following beneficial effects.
1. The method for measuring the lumped electrical parameters of the solenoid micro-coil adopts a TRL de-embedding method, designs a corresponding calibration piece according to a manufactured clamp, establishes a 10-item error model for measuring S parameters of a piece to be measured by a vector network analyzer, obtains the S parameters of the solenoid micro-coil without the influence of the clamp through formula derivation, and greatly reduces errors brought by the measuring clamp.
2. According to the method for measuring the lumped electrical parameters of the solenoid micro-coil, the Z parameters are obtained through S parameter conversion of the solenoid micro-coil, then the lumped electrical parameters are obtained through the Z parameters and an equivalent circuit model by using a nonlinear least square fitting method, and the lumped electrical parameters of the solenoid micro-coil with the working frequency in a GHz range can be obtained instead of a method of directly measuring the lumped electrical parameters through an LCR tester or directly measuring the Z parameters through impedance analysis.
3. The method for measuring the lumped electrical parameters of the solenoid micro-coil provided by the invention adopts the manufactured clamp and the manufactured calibration piece, and can measure the lumped electrical parameters of the solenoid micro-coil with the dimension of mm.
Drawings
FIG. 1 is a flow chart of a solenoid microcoil lumped electrical parameter measurement method;
FIG. 2 is a block diagram of a DUT clamp welding solenoid microcoil under test;
FIG. 3 is a schematic diagram of a PCB design of a DUT clamp, straight-through (T) -reflection (R) -transmission line (L) calibration piece;
FIG. 4 is a signal flow diagram of a 10 term error model of a solenoid microcoil dut;
FIG. 5 is a circuit diagram of a solenoid micro-coil lumped equivalent circuit model;
reference numerals:
201. the calibration device comprises a radio frequency connector 202, a printed circuit board 203, a microstrip line 204, a base 205, a solenoid micro-coil to be tested 301, a PCB of a DUT clamp 302, a PCB of a through calibration piece 303, a PCB of a reflection calibration piece 304 and a PCB of a transmission line calibration piece.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides a method for measuring lumped electrical parameters of a solenoid micro-coil, which comprises the following steps:
the clamp is designed according to the size of the solenoid micro-coil to be tested, and comprises a radio frequency connector, a printed circuit board, two sections of microstrip lines with the same length and a base. Welding the solenoid micro-coil to be tested between two sections of microstrip lines of the clamp to form a solenoid micro-coil to be tested; designing and manufacturing a calibration piece according to the structural size of the piece to be tested of the solenoid coil, wherein the calibration piece comprises a direct calibration piece, a reflection calibration piece and a transmission line calibration piece;
respectively measuring S parameter matrixes of a solenoid micro-coil to-be-measured piece and a calibration piece;
calculating an S parameter matrix of the solenoid micro coil to be measured according to the S parameter matrices of the solenoid micro coil to be measured and the calibration piece by using a TRL de-embedding method, obtaining the resonance frequency and the quality factor of the solenoid micro coil, and obtaining a Z parameter matrix of the solenoid micro coil by using the corresponding relation of the S parameter and the Z parameter;
and obtaining the equivalent series resistance, the equivalent inductance and the equivalent parallel capacitance of the solenoid micro-coil by utilizing a nonlinear least square fitting method according to the Z parameter matrix.
The flow of the solenoid microcoil lumped electrical parameter measurement of the present invention is illustrated in fig. 1 and described in detail below.
Step 101: the PCB of the DUT fixture is designed according to the geometric size of the solenoid micro-coil and the characteristic impedance requirements of the microstrip line. As shown in fig. 2, the DUT clamp is composed of a radio frequency connector 201, a printed circuit board 202, a microstrip line 203, and a base 204. The radio frequency connector 201 is used for connecting a network analyzer; the substrate of the printed circuit board 202 is a radio frequency printed circuit board base material and has the three characteristics of high hardness, small dielectric constant and small loss factor; the base 204 is used for fixing the substrate and grounding. After the DUT fixture is fabricated, the solenoid microcoil 205 to be tested is soldered to the DUT fixture.
Step 102: and respectively manufacturing a through (T, Thru) calibration piece, a reflection (R, reflex) calibration piece and a transmission Line (L, Line) calibration piece. The pass-through calibration piece, the reflection calibration piece, the transmission line calibration piece and the DUT clamp are identical in structure. As shown in fig. 3, 301 is the PCB of the DUT clamp, 203 is a microstrip line, 205 is a solenoid microcoil to be tested, 302 is the PCB of the through calibration piece, 303 is the PCB of the reflection calibration piece, and 304 is the PCB of the transmission line calibration piece. The length of the microstrip line of the PCB 302 of the through calibration piece is equal to that of the microstrip line of the PCB301 of the DUT clamp, the characteristic impedance of the microstrip line is the same as that of the microstrip line 203 of the DUT clamp, the transmission coefficient is 1, and the reflection coefficient is 0. The PCB 303 of the reflection calibration part completes reflection in a short circuit mode, the length of microstrip lines at two ends of the reflection calibration part is half of that of the microstrip line of the PCB301 of the DUT clamp, the transmission coefficient of the reflection calibration part is 0, and the reflection coefficient of the reflection calibration part is-1. The phase difference between the microstrip line of the PCB 304 of the transmission line calibration piece and the microstrip line of the PCB 302 of the through calibration piece is between 20 ° and 160 °, and the length of the microstrip line is generally a quarter wavelength (1/4 λ) added on the basis of the length of the microstrip line of the through calibration piece PCB 302, and the characteristic impedance of the microstrip line is the same as the impedance of the microstrip line of the DUT fixture.
And 103, respectively measuring S parameter matrixes of a solenoid micro-coil to-be-measured element (DUT), the straight-through (T) calibration element, the reflection (R) calibration element and the transmission line (L) calibration element by using a network analyzer.
And step 104, calculating the estimated value of the S parameter matrix of the solenoid micro-coil to be measured by using a TRL de-embedding method according to the four groups of S parameter matrices measured in the step 103.
And 105, acquiring the resonance frequency and the quality factor of the solenoid micro-coil through the S parameter estimation value, and acquiring the estimation value of the Z parameter matrix of the solenoid micro-coil by utilizing the corresponding relation between the S parameter and the Z parameter of the two-port network.
And step 107, obtaining the estimated values of the equivalent series resistance, the equivalent inductance and the equivalent parallel capacitance of the solenoid micro-coil by a nonlinear least square fitting method or electronic design automation software ADS according to the estimated value of the S parameter matrix of the solenoid micro-coil and the collective equivalent circuit model.
Specifically, in step 101, the characteristic impedance of the DUT clamp is 50 ohms; the radio frequency connector 201 selects an SMA interface; the substrate is selected from an RO4350 plate or a TLX-7 plate; the base is made of aluminum or steel.
The formula for calculating the characteristic impedance of the microstrip line in the step 101 and the step 102 is as follows:
wherein epsilonrIs the relative dielectric constant, epsilon, of the PCB substrate boardeffIs an equivalent dielectric constant, Z0For characteristic impedance, h is the substrate thickness and w is the microstrip line width.
The calculation formula for calculating the wavelength λ in the step 102 is:
wherein c is the speed of light, εeffIs an equivalent dielectric constant, f0The center frequency of the working frequency band, or the approximate resonance frequency of the solenoid micro-coil to be tested, can be calculated by Q3D extra simulation software.
In step 103, the solenoid micro-coil to be tested is welded on the DUT fixture, and a signal flow diagram of a 10-term error model of the piece to be tested is shown in fig. 4. Wherein e30Is a positive leakage error, e03Is a negative leakage error, e11Is a positive match error, e22Is a negative match error, e10e01Is the forward reflection frequency response error, e23e32Is a negative reflection frequency response error, e10e32Is the forward transmission frequency response error, e23e01Is a negative transmission frequency response error, e00Is a forward direction error, e33Is a negative direction error.
According to fig. 4 and Mason formula, the relationship between the S parameter matrix measurement value of the to-be-measured piece and the S parameter matrix estimation value of the to-be-measured solenoid micro-coil can be obtained as follows:
wherein, s'11、s′21、s′22、s′12The measured value of the S parameter matrix of the solenoid micro-coil to-be-measured piece is obtained; s11、S21、S22、S12Is the estimated value of the S parameter matrix of the solenoid micro-coil to be tested.
Straight-through (T) calibration: a direct connection calibration part is connected between the two test ports, and an S parameter is equivalently connected21＝S12＝1，S11＝S22A network of 0, thus yielding:
wherein, T11、T21、T22、T12Respectively representing the through calibration piece S parameters (S)11)T、(S21)T、(S22)T、(S12)TIs measured.
Reflectance (R) calibration: a reflection calibration piece is connected between the two test ports (reflection is completed in a short circuit mode), and an S parameter S is equivalently connected21＝S12＝0，S11＝S22A network of-1, thereby obtaining:
R21＝e30
R12＝e03
wherein R is11、R21、R22、R12Respectively representing the parameters (S) of the reflective calibration piece11)R、(S21)R、(S22)R、(S12)RIs measured.
Transmission line (L) calibration: a transmission line calibration piece is connected between the two test ports, and an S parameter S is equivalently connected11＝S22＝0，S21＝S12＝e-jβlThereby obtaining:
wherein beta is the phase constant, L is the electrical length of the microstrip line, L11、L21、L22、L12Respectively representing the S parameters (S) of the transmission line calibration piece11)L、(S21)L、(S22)L、(S12)LIs measured.
By combining the above equations, the de-embedding data processing algorithm model for deriving the S parameter of the solenoid micro-coil is:
e30＝R21
e03＝R12
the lumped equivalent circuit model in step 106 is shown in fig. 5. Wherein R issIs the equivalent series resistance of the solenoid micro coil to be tested, L is the equivalent inductance of the solenoid micro coil to be tested,Cpis the equivalent parallel capacitance of the solenoid micro-coil under test.
Specifically, in step 107, the lumped electrical parameters of the solenoid micro-coil can be directly obtained from the S-parameter matrix through the electronic design automation software ADS, and the S-parameter does not need to be converted into the Z-parameter. The specific process is as follows:
firstly, according to fig. 5, a lumped equivalent circuit model of the solenoid micro-coil is established, two ports of the model are port1 and port2, the S2P file corresponding to the estimated value of the S parameter matrix of the solenoid micro-coil obtained in the step 104 is imported into the ADS software, the ports of the two-port network are port3 and port4, and an optimization function (optimal) module is utilized to lead R in the equivalent model to be port3 and port4s、L、CpSetting four optimization targets S with weights of 1 as optimization variables11-S33＝0、S12-S34＝0、S21-S43＝0、S22-S440. After the operation is completed, the optimization is clicked, and the optimal solution obtained after the optimization is finished can be regarded as the lumped electrical parameter of the solenoid micro-coil. Through experimental verification, the high-frequency resistance value of the solenoid micro-coil obtained by measurement by using the method is compared with the simulated resistance value, and the relative error is 2%; the relative error between the inductance value and the simulated inductance value is 4.5 percent; the relative error between the high-frequency capacitance value and the simulated capacitance value is 2.2 percent; the relative error between the resonant frequency and the simulated resonant frequency is 0.1 percent; the relative error between the quality factor and the simulated quality factor is 5.9%, so that the requirement of practical application can be well met.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (7)
1. A method for measuring lumped electrical parameters of a solenoid microcoil, comprising the steps of:
designing a clamp according to the size of the solenoid micro-coil to be tested, wherein the clamp comprises two microstrip lines with the same length, and the solenoid micro-coil to be tested is welded between the two microstrip lines of the clamp to form a solenoid micro-coil to be tested; determining a calibration piece according to the piece to be tested of the solenoid coil, wherein the calibration piece comprises a direct calibration piece, a reflection calibration piece and a transmission line calibration piece;
respectively measuring S parameter matrixes of a solenoid micro-coil to-be-measured piece and a calibration piece;
calculating an S parameter matrix of the solenoid micro coil to be measured according to the S parameter matrices of the solenoid micro coil to be measured and the calibration piece by using a TRL de-embedding method, obtaining the resonance frequency and the quality factor of the solenoid micro coil, and obtaining a Z parameter matrix of the solenoid micro coil by using the corresponding relation of the S parameter and the Z parameter;
and obtaining the equivalent series resistance, the equivalent inductance and the equivalent parallel capacitance of the solenoid micro-coil by utilizing a nonlinear least square fitting method according to the Z parameter matrix.
2. The method according to claim 1, wherein the straight-through calibration member comprises a microstrip line having a length equal to the sum of the lengths of two microstrip lines of the solenoid micro-coil device under test, and has a transmission coefficient of 1 and a reflection coefficient of 0.
3. The method according to claim 1, wherein the reflection calibration piece comprises two microstrip lines, the length of each microstrip line is the same as that of the microstrip line of the solenoid micro-coil device under test, and the transmission coefficient and the reflection coefficient of the straight-through calibration piece are respectively 0 and-1.
4. The method of claim 1, wherein the transmission line calibration element comprises a microstrip line having a length greater than that of the solenoid microcoil device under test, and wherein the transmission line calibration element has a transmission phase delay of between 20 ° and 160 ° with respect to the feedthrough calibration element.
5. The measurement method according to claim 1, wherein the S parameter matrix of the solenoid microcoil under test:
wherein, s'11、s′21、s′22、s′12Measured values of an S-parameter matrix for a solenoid micro-coil test piece, e30Is a positive leakage error, e03Is a negative leakage error, e11Is a positive match error, e22Is a negative match error, e10e01Is the forward reflection frequency response error, e23e32Is a negative reflection frequency response error, e10e32Is the forward transmission frequency response error, e23e01Is a negative transmission frequency response error, e00Is a forward direction error, e33Is a negative direction error.
6. The measurement method according to claim 5,
e30＝R21
e03＝R12
wherein, T11、T21、T22、T12Respectively representing measured values, R, of a matrix of S-parameters of said pass-through calibration member11、R21、R22、R12Respectively representing the measured values of the S-parameter matrix of the reflective calibration member, L11、L21、L22、L12Respectively representing the measured values of the S parameter matrix of the transmission line calibration piece.
7. The measurement method according to claim 1, wherein the microstrip line is a metal.
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Application publication date: 20220114 |