An inductance value measurement and traceability device and method

Abstract

This invention provides an inductance measurement and traceability device and method. The measuring device includes a bridge circuit. In the bridge circuit, the -1 terminal of the bridge power supply is connected to the bridge auxiliary balancing network and the bridge arm unit in sequence via wires, and then connected to the +1 terminal of the bridge power supply. The bridge arm unit includes a first null pointer, a second null pointer, and four bridge arms. The first bridge arm contains the inductance to be measured and a first resistor (equivalent series resistance). The second bridge arm contains a second resistor. The fourth bridge arm contains a fourth resistor. The third bridge arm contains a first inductive voltage divider, a second inductive voltage divider, a first conductance, and a first capacitor. The inductance value traceability method connects a 1:-1 inductive voltage divider to the output terminal of the first inductive voltage divider and uses a standard capacitor to replace the inductance to be measured. At a specific frequency, through impedance transformation technology, a capacitor with the same nominal impedance is used to replace the inductance to be measured, thereby achieving direct traceability of the inductance value to the capacitance unit.

Description

Technical Field

[0001] The present invention relates to the technical field of precision electromagnetic measurement, and in particular to an inductance value measurement and tracing device and method. Background Art

[0002] Inductance parameters are used to measure the ability of a coil to generate electromagnetic induction. They are important physical quantities in electromagnetic metrology. The unit of inductance, Henry (H), is a derived unit of the International System of Units (SI). Inductance devices of different sizes and scales are widely used in industries such as electricity, transportation, aerospace, electronics, and communications. Their quality depends on the inductance value and Q value at different frequencies. It is of great significance to ensure the accurate transmission of the inductance value.

[0003] my country's inductance reference device consists of an inductance reference (Sullivan) and an AC resonant bridge. It reproduces the inductance value at 1kHz, with an uncertainty of 5×10 -6 (k=1), and participated in the CCEM-K3 international comparison in 1990 and obtained international equivalence. Using the resonance method to reproduce the inductance value is to trace the inductance value directly to the capacitance unit, which has the advantage of a short traceability link. However, the resonance method is easily affected by the line distribution parameters, and the accuracy of inductance value reproduction is difficult to improve. And due to the influence of line aging, the benchmark device has been out of service for many times since the 1990s.

[0004] Under the new SI system of units, the absolute measurement of electrical AC impedance units, that is, the reproduction of SI units of resistance, capacitance, and inductance, can still be achieved by the method of reproducing impedance units by calculating capacitance.

[0005] my country's new generation of inductance reference devices uses the Maxwell-Wien bridge method to reproduce inductance values. At present, the mainstream national metrology institutes in the world (such as Australia's NMIA, Britain's NPL, and Germany's PTB) all use the Maxwell-Wien bridge method to reproduce inductance values, tracing the inductance values ​​to AC resistance and capacitance units, and the reproduction level is mostly around 5-10μH / H (k=1). The Italian Institute of Metrology (IEN) uses the three-voltage method to directly trace the inductance to the AC resistance, shortening the traceability link, and the extended measurement uncertainty of the value reproduction is 13μH / H (k=2).

[0006] In the prior art, the conventional Maxwell-Wien bridge method for reproducing the bridge circuit of the inductance value has room for improvement in the measurement accuracy of the inductance, and the existing traceability method cannot directly trace the inductance value to the capacitance unit. Summary of the invention

[0007] In order to solve the above problems, the present invention provides an inductance value measurement and tracing device and method to overcome the shortcomings of the resonance method, directly trace the inductance value to the capacitance unit, and at a specific frequency, through impedance transformation technology, use a capacitor with the same impedance nominal value to replace the measured inductance for measurement, thereby achieving direct tracing of the inductance value to the capacitance unit.

[0008] In order to achieve the above object, the present invention provides an inductance value measurement and traceability device and method, and the technical solution adopted is as follows:

[0009] According to a first aspect of the present invention, there is provided an inductance value measuring device, comprising a bridge circuit, wherein the bridge circuit comprises a bridge power supply, a bridge auxiliary balancing network and a bridge arm unit;

[0010] The -1 end of the bridge power supply is connected to the bridge auxiliary balance network and the bridge arm unit in sequence through a wire and then connected to the +1 end of the bridge power supply;

[0011] The bridge arm unit includes a first zero pointer, a second zero pointer and four bridge arms, the four bridge arms are respectively a first bridge arm, a second bridge arm, a third bridge arm and a fourth bridge arm, the first bridge arm is provided with a measured inductance and a first resistor (equivalent series resistor), the second bridge arm is provided with a second resistor, the fourth bridge arm is provided with a fourth resistor, the third bridge arm is provided with a first inductive voltage divider, a second inductive voltage divider, a first conductance and a first capacitor, the first capacitor is provided on the line connecting the first inductive voltage divider and the fourth bridge arm, and the first conductance is provided on the line connecting the second inductive voltage divider and the fourth bridge arm.

[0012] Furthermore, the bridge auxiliary balancing network includes a multi-disk inductive voltage divider and a second inductor and a second capacitor connected to the multi-disk inductive voltage divider.

[0013] Furthermore, when the readings of the first zero indicator and the second zero indicator are both zero, the bridge circuit reaches a balanced state and has an inductance balance relationship as shown in formula (1):

[0014] L1=αR2R4C S ,R1=βR2R4G S (1)

[0015] Where L1 represents the inductance of the inductor under test, R1, R2 and R4 represent the resistance values ​​of the first resistor, the second resistor and the third resistor respectively, α represents the measured value of the inductor under test, β represents the measured value of the equivalent series resistance of the inductor under test, and C s Represents the capacitance value of the first capacitor, G s represents the conductance value of the first conductance.

[0016] Furthermore, when the bridge circuit reaches a balanced state, considering the influence of the time constant of the second resistor, the third resistor and the first conductance in the bridge circuit, the inductance balance relationship of the bridge circuit is shown in formula (2):

[0017]

[0018] In the formula, τ1, τ2, τ4 and τ G Represent the time constants of the first resistance, the second resistance, the third resistance and the first conductance respectively.

[0019] According to a second aspect of the present invention, a method for tracing the inductance value is provided, characterized in that, based on the inductance value measuring device as described above, the tracing method comprises:

[0020] Connect a 1:-1 inductive voltage divider to the output end of the first inductive voltage divider;

[0021] A standard capacitor is used to replace the inductor to be measured, and the capacitance value of the standard capacitor satisfies 1 / ω. 2 C x ≈L1, where ω represents the angular frequency, C x Indicates the capacitance value of a standard capacitor.

[0022] Furthermore, when a standard capacitor is used to replace the measured inductance for measurement, the inductance balance relationship of the bridge circuit is expressed as:

[0023]

[0024] Where α' and β' represent the measured inductance and equivalent series resistance of the standard capacitor when a standard capacitor is used to replace the inductance under test, respectively, and δ represents the ratio error of the 1:-1 inductive voltage divider with a 10nF load on both ends of the ±1 circuit.

[0025] Furthermore, the method further includes: calculating the measured inductance value L1 by the following formula:

[0026]

[0027] According to a third aspect of the present invention, there is provided an inductance value tracing device, comprising a bridge circuit, wherein the bridge circuit comprises a bridge power supply, a bridge auxiliary balancing network and a bridge arm unit;

[0028] The -1 end of the bridge power supply is connected to the bridge auxiliary balance network and the bridge arm unit in sequence through a wire and then connected to the +1 end of the bridge power supply;

[0029] The bridge arm unit comprises a first zero pointer, a second zero pointer and four bridge arms, wherein the four bridge arms are respectively a first bridge arm, a second bridge arm, a third bridge arm and a fourth bridge arm, wherein the first bridge arm is provided with two first loops and a second loop connected in parallel, wherein the first loop is provided with a measured inductance and a first resistor, the second loop is provided with a standard capacitor, the second bridge arm is provided with a second resistor, the fourth bridge arm is provided with a fourth resistor, the third bridge arm is provided with a first inductive voltage divider, a second inductive voltage divider, a first conductance, a first capacitor and a 1:-1 inductive voltage divider, the 1:-1 inductive voltage divider and the first capacitor are provided on the line connecting the first inductive voltage divider and the fourth bridge arm, and the first conductance is provided on the line connecting the second inductive voltage divider and the fourth bridge arm;

[0030] The capacitance value of the standard capacitor satisfies 1 / ω 2 C x ≈L1, where ω represents the angular frequency, C x It represents the capacitance value of the standard capacitor, and L1 represents the inductance value being measured.

[0031] Furthermore, when a standard capacitor is used to replace the measured inductance for measurement, the inductance balance relationship of the bridge circuit is expressed as:

[0032]

[0033] Where R1, R2 and R4 represent the resistance values ​​of the first resistor, the second resistor and the third resistor respectively, α represents the measured value of the inductor under test, β represents the measured value of the equivalent series resistance of the inductor under test, and C s Represents the capacitance value of the first capacitor, G s represents the conductance value of the first conductance, α' and β' represent the measured inductance value and the equivalent series resistance value of the standard capacitor when a standard capacitor is used to replace the measured inductance for measurement, and δ represents the ratio error of the 1:-1 inductive voltage divider with a 10nF load at both ±1 ends.

[0034] Furthermore, the measured inductance value L1 is calculated by the following formula:

[0035]

[0036] The present invention has at least the following beneficial effects:

[0037] 1. Use the traceable and calibrated capacitance value C x , which can realize a Maxwell-Wien bridge standard value R2R4C s Calibration method.

[0038] 2. Different from conventional methods, the inductance value can be directly traced back to the capacitance unit, shortening the value transmission link. At the same time, the results of the method proposed in the present invention can also verify the results of reproducing the inductance unit using the conventional Maxwell-Wien bridge method. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for the specific embodiments or the description of the prior art. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn according to the actual scale.

[0040] Figure 1 A circuit structure diagram of an inductance value measuring device according to an embodiment of the present invention is shown.

[0041] Figure 2 A circuit structure diagram of an inductance value tracing device according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0042] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0043] In the description of the present invention, unless otherwise specified, "plurality" means two or more than two; the orientations or positional relationships indicated by the terms "upper", "lower", "left", "right", "inner", "outer", "front end", "rear end", "head", "tail", etc. are based on the orientations or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", "third", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0044] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "connected" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0045] The specific implementation of the present invention is further described in detail below in conjunction with the drawings and examples.

[0046] Embodiment 1:

[0047] The embodiment of the present invention provides an inductance value measuring device, such as Figure 1 As shown, the inductance value measuring device includes a bridge circuit, and the bridge circuit includes a bridge power supply, a bridge auxiliary balancing network and a bridge arm unit; the -1 end of the bridge power supply is connected to the bridge auxiliary balancing network and the bridge arm unit in sequence through a wire and then connected to the +1 end of the bridge power supply; the bridge arm unit includes a first zero indicator D1, a second zero indicator D2 and four bridge arms, and the four bridge arms are respectively a first bridge arm, a second bridge arm, a third bridge arm and a fourth bridge arm, the first bridge arm is provided with a measured inductance L1 and a first resistor R1, the second bridge arm is provided with a second resistor R2, the fourth bridge arm is provided with a fourth resistor R4, and the third bridge arm is provided with a first inductive voltage divider IVDα, a second inductive voltage divider IVDβ, a first inductive voltage divider G s and the first capacitor C s The first capacitor C is set on the line connecting the first inductive voltage divider IVDα and the fourth bridge arm s The first conductive resistor G is set on the line connecting the second inductive voltage divider IVDβ and the fourth bridge arm. s .

[0048] It should be noted that Figure 1 The identification symbols involving electronic components not only indicate the corresponding electronic components, but also represent the parameter values ​​of the electronic components they indicate in the formula calculation. For example, R1 is used to indicate the first resistor and also represents the resistance value of the first resistor in the formula.

[0049] In this embodiment, the inductor L1 and the resistor R1 in the four bridge arms of the bridge arm unit are the measured inductor and its equivalent series resistance, the resistors R2 and R4 are AC standard resistors (different bridge arm resistors are selected for different inductance ranges), the first inductive voltage divider IVDα and the standard capacitor C s Used to balance the inductance component being measured, the second inductive voltage divider IVDβ and the conductance G sIt is used to balance the equivalent series resistance component of the inductor being measured. The indicated value α of IVDα represents the measured value of the inductor being measured, and the indicated value β of IVDβ represents the measured value of the equivalent series resistance of the inductor being measured.

[0050] Exemplarily, the first inductive voltage divider IVDα and the second inductive voltage divider IVDβ may be selected as seven-disc double-stage inductive dividers, and the first nulling instrument D1 and the second nulling instrument D2 may be selected as phase-locked amplifiers.

[0051] The output end of the bridge power supply -1 is connected to an AC combination network consisting of a multi-disc inductive voltage divider plus a second inductor G and a second capacitor C. This branch is called the bridge auxiliary balance (power balance) network. When the bridge is working, adjusting the auxiliary balance network can make the bridge's zero-pointing terminal a tend to the ground potential, preventing current leakage at the zero-pointing instrument end, that is, achieving bridge power balance. When the auxiliary balance network is adjusted to make the reading of the second zero-pointing instrument D2 point to zero, and at the same time adjusting IVDα and IVDβ to make the reading of the first zero-pointing instrument D1 point to zero, that is, the auxiliary balance and main balance of the bridge circuit reach a balanced state at the same time, there is the following relationship:

[0052] L1=αR2R4C S ,R1=βR2R4G S (1)

[0053] In the formula, R2R4C S and R2R4G S It is called the standard value of the bridge. When the bridge is balanced, the inductance value L1 and the equivalent series resistance value R1 of the inductor under test can be calculated through the α and β readings and the standard value of the bridge, thus realizing the traceability of the inductance value to the AC resistance and capacitance units.

[0054] From formula (1), we can see that α, R2, R4 and C s It is the key parameter that determines the value of the inductance being measured. The standard resistors R2 and R4 of the inductance reference device are high-precision AC standard resistors (Vishay units), and the standard capacitor C s This is achieved using custom temperature-controlled multilayer ceramic capacitors (NP0 / C0G capacitors). The parameter configuration of the bridge impedance standard is shown in Table 1.

[0055] Table 1 Inductor reference transfer bridge parameter configuration

[0056] Range <![CDATA[R2]]> <![CDATA[R4]]> <![CDATA[G s -1 ]]> <![CDATA[C s ]]> 10mH 1kΩ 1kΩ 50kΩ 10nF 100mH 10kΩ 1kΩ 100kΩ 10nF

[0057] The time constant of the AC standard resistor will affect the balance relationship of the bridge. If the AC standard resistors R2, R4 and G in the bridge are considered s The influence of the time constant, Figure 1 The inductance balance relationship of the bridge becomes:

[0058]

[0059] It can be seen from formula (2) that the time constant of the standard AC resistance of the bridge arm has an impact on the measured inductance value. In order to accurately reproduce the inductance value using the Maxwell-Wien bridge method, it is also necessary to accurately measure the impact introduced by the time constant of the bridge AC resistance.

[0060] Embodiment 2:

[0061] An embodiment of the present invention provides an inductance value tracing method. Based on the inductance value measuring device as described in Embodiment 1, the tracing method includes:

[0062] The inductance (L1 and R1) of the inductor to be measured is connected to the inductance value measuring device of Example 1, and the inductance L1 and R1 to be measured are directly measured. The inductance L1 to be measured can be obtained as shown in formula (2).

[0063] A 1:-1 inductive voltage divider is connected to the output end of the first inductive voltage divider; a standard capacitor is then used to replace the inductor to be measured, and the capacitance value of the standard capacitor satisfies 1 / ω 2 C x ≈L1, where ω represents the angular frequency, C x Indicates the capacitance value of a standard capacitor.

[0064] According to the inductance value tracing method, an inductance value tracing device can be obtained, such as Figure 2 As shown, the inductance value tracing device includes a bridge circuit, which includes a bridge power supply, a bridge auxiliary balancing network and a bridge arm unit; the -1 end of the bridge power supply is connected to the bridge auxiliary balancing network and the bridge arm unit in sequence through a wire and then connected to the +1 end of the bridge power supply; the bridge arm unit includes a first zero indicator D1, a second zero indicator D2 and four bridge arms, and the four bridge arms are respectively a first bridge arm, a second bridge arm, a third bridge arm and a fourth bridge arm, and the first bridge arm is provided with two parallel first loops and a second loop, wherein the first loop is provided with a measured inductance L1 and a first resistor R1, and the second loop is provided with a standard capacitor C x The second bridge arm is provided with a second resistor R2, the fourth bridge arm is provided with a fourth resistor R4, the third bridge arm is provided with a first inductive voltage divider IVDα, a second inductive voltage divider IVDβ, a first conductive G s The first capacitor C s and a 1:-1 inductive voltage divider, the 1:-1 inductive voltage divider and the first capacitor C are arranged on the line connected to the first inductive voltage divider IVDα and the fourth bridge arm. s The first conductive resistor G is set on the line connecting the second inductive voltage divider IVDβ and the fourth bridge arm. s .

[0065] Use a standard capacitor Cx Replace the inductor to be measured. If the standard capacitor C x The value of satisfies 1 / ω 2 C x ≈L1, after the bridge is balanced, the balance relationship can be obtained:

[0066]

[0067] Where α' and β' represent the measured inductance and equivalent series resistance of the standard capacitor when a standard capacitor is used to replace the inductance under test, respectively, and δ represents the ratio error of the 1:-1 inductive voltage divider with a 10nF load on both ends of the ±1 circuit.

[0068] Since the standard capacitance C x The loss is very small, so its equivalent series resistance is also very small, and its size is equal to β′R2R4G s , so the second term on the right side of formula (3) can be ignored. By calculation, the standard value of the bridge R2R4C s , combined with formula (1), the measured inductance value can be obtained:

[0069]

[0070] Since the readings of α and α' are basically the same, that is, the standard capacitor is used to replace the measured inductance, and a new traceability method is realized that can directly trace the inductance value to the capacitance unit. This method shortens the traceability chain of the inductance value. In essence, it calibrates the standard value of the bridge under working conditions, so it can be used to verify the results of reproducing the inductance value by the Maxwell-Wien bridge method.

[0071] At 1kHz, the standard capacitor C x The 100mH standard inductor is used for substitution measurement. In order to make the two IVDα readings as consistent as possible, C x It is a temperature-controlled standard capacitor with a nominal value of 253.303nF. Its value is compared with a 10nF capacitor through a four-terminal capacitance bridge that can achieve any ratio, and its value is traceable to a new generation of calculated capacitance reference device.

[0072] After experimental verification, the Maxwell-Wien bridge method and the method based on capacitor substitution were used to reproduce the inductance unit. At 1kHz, the measurement uncertainty of the two methods for reproducing the inductance value was better than 2μH / H (k=1), and the relative error of the two methods for reproducing the 100mH inductance value was less than 1×10 -6 , the two devices are mutually authenticated.

[0073] The above implementation modes are only used to illustrate the present invention, but not to limit the present invention. Ordinary technicians in the relevant technical field can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, all equivalent technical solutions also belong to the scope of the present invention. The patent protection scope of the present invention should be defined by the claims.

Claims

1. A method for tracing the source of inductance value, characterized in that: Based on an inductance value measuring device, the bridge circuit includes a bridge power supply, a bridge auxiliary balancing network and a bridge arm unit; The -1 end of the bridge power supply is connected to the bridge auxiliary balance network and the bridge arm unit in sequence through a wire and then connected to the +1 end of the bridge power supply; The bridge arm unit comprises a first zero pointer, a second zero pointer and four bridge arms, the four bridge arms are respectively a first bridge arm, a second bridge arm, a third bridge arm and a fourth bridge arm, the first bridge arm is provided with a measured inductance and a first resistor, the second bridge arm is provided with a second resistor, the fourth bridge arm is provided with a fourth resistor, the third bridge arm is provided with a first inductive voltage divider, a second inductive voltage divider, a first conductance and a first capacitor, the first capacitor is provided on a line connecting the first inductive voltage divider and the fourth bridge arm, and the first conductance is provided on a line connecting the second inductive voltage divider and the fourth bridge arm; The traceability method includes: Connect a 1:-1 inductive voltage divider to the output end of the first inductive voltage divider; A standard capacitor is used to replace the inductor to be measured, and the capacitance value of the standard capacitor satisfies 1 / ω. 2 C x ≈L1, where ω represents the angular frequency, C x Indicates the capacitance value of a standard capacitor; When a standard capacitor is used to replace the inductor to be measured, the inductance balance relationship of the bridge circuit is expressed as: Where α′ and β′ represent the measured inductance and the equivalent series resistance of the standard capacitor when a standard capacitor is used to replace the measured inductance, respectively. δ represents the ratio error of the 1:-1 inductive voltage divider with a 10nF load at both ends of the ±1 circuit. The method further includes: calculating the measured inductance value L1 by the following formula:

2. The inductance value tracing method according to claim 1, characterized in that: The bridge auxiliary balancing network includes a multi-disk inductive voltage divider, a second inductor and a second capacitor connected to the multi-disk inductive voltage divider.

3. The inductance value tracing method according to claim 1, characterized in that: When the readings of the first zero indicator and the second zero indicator are both zero, the bridge circuit reaches a balanced state and has an inductance balance relationship as shown in formula (1): L1=αR2R4C S ,R1=βR2R4G S (1) Where L1 represents the inductance value of the inductor under test, R1, R2 and R4 represent the resistance values ​​of the first resistor, the second resistor and the third resistor respectively, α represents the measured reading of the inductor under test, β represents the measured reading of the equivalent series resistance of the inductor under test, and C s Represents the capacitance value of the first capacitor, G s represents the conductance value of the first conductance.

4. The inductance value tracing method according to claim 1, characterized in that: When the bridge circuit reaches a balanced state, considering the influence of the time constant of the second resistor, the third resistor and the first conductance in the bridge circuit, the inductance balance relationship of the bridge circuit is shown in formula (2): In the formula, τ1, τ2, τ4 and τ G Represent the time constants of the first resistance, the second resistance, the third resistance and the first conductance respectively.

5. An inductance value tracing device, characterized in that: The invention comprises a bridge circuit, wherein the bridge circuit comprises a bridge power supply, a bridge auxiliary balancing network and a bridge arm unit; The -1 end of the bridge power supply is connected to the bridge auxiliary balance network and the bridge arm unit in sequence through a wire and then connected to the +1 end of the bridge power supply; The bridge arm unit comprises a first zero pointer, a second zero pointer and four bridge arms, wherein the four bridge arms are respectively a first bridge arm, a second bridge arm, a third bridge arm and a fourth bridge arm, wherein the first bridge arm is provided with two first loops and a second loop connected in parallel, wherein the first loop is provided with a measured inductance and a first resistor, the second loop is provided with a standard capacitor, the second bridge arm is provided with a second resistor, the fourth bridge arm is provided with a fourth resistor, the third bridge arm is provided with a first inductive voltage divider, a second inductive voltage divider, a first conductance, a first capacitor and a 1:-1 inductive voltage divider, the 1:-1 inductive voltage divider and the first capacitor are provided on the line connecting the first inductive voltage divider and the fourth bridge arm, and the first conductance is provided on the line connecting the second inductive voltage divider and the fourth bridge arm; The capacitance value of the standard capacitor satisfies 1 / ω 2 C x ≈L1, where ω represents the angular frequency, C x Indicates the capacitance value of the standard capacitor, L1 indicates the inductance value being measured; When a standard capacitor is used to replace the inductor to be measured, the inductance balance relationship of the bridge circuit is expressed as: Where R1, R2 and R4 represent the resistance values ​​of the first resistor, the second resistor and the third resistor respectively, α represents the measured value of the inductor under test, β represents the measured value of the equivalent series resistance of the inductor under test, and C s Represents the capacitance value of the first capacitor, G s represents the conductance value of the first conductance, α′ and β′ represent the measured inductance value and the equivalent series resistance value of the standard capacitor when a standard capacitor is used to replace the measured inductance for measurement, and δ represents the ratio error of the 1:-1 inductive voltage divider with 10nF load at both ±1 ends; The measured inductance value L1 is calculated by the following formula:

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