Method for measuring coupling coefficients, system for measuring coupling coefficients, and program
By measuring and calculating coupling coefficients at the zero-current timing, the method addresses inaccuracies in low-Q coil measurements, ensuring precise coupling coefficient determination.
Patent Information
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- TOKYO METROPOLITAN PUBLIC UNIVERSITY CORPORATION
- Filing Date
- 2024-11-20
- Publication Date
- 2026-06-01
AI Technical Summary
Existing methods for measuring coupling coefficients in transformers yield inaccurate results when the coil quality factor Q is low, leading to incorrect calculations.
Measure the current flowing through the primary winding, the voltage between the endpoints of the primary winding, and the voltage between the endpoints of the secondary winding when an alternating current is output to the primary winding, and calculate the coupling coefficient based on these values at the timing when the current becomes zero.
Enables accurate calculation of coupling coefficients even when the coil quality factor is low, providing consistent results regardless of the coil's quality factor.
Smart Images
Figure 2026089517000001_ABST
Abstract
Description
[Technical Field]
[0001] This invention relates to a method for measuring coupling coefficients, a system for measuring coupling coefficients, and a program. [Background technology]
[0002] The coupling coefficient is a numerical value that represents the degree of magnetic coupling between two coils. It is an important parameter that determines the leakage flux of a transformer and affects the transformation ratio. The coupling coefficient as a function of frequency is called the coupling coefficient frequency characteristic.
[0003] To measure the frequency characteristics of the coupling coefficient, the open-circuit method described in JIS C5321 is commonly used. This method is frequently used because it allows for easy measurement while varying the frequency. The open-circuit method measures the inductance L of the primary winding when the secondary winding of the transformer is open-circuited and when it is short-circuited. open , L short This method involves measuring and calculating the coupling coefficient k from equation (1).
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[0004] However, the coupling frequency characteristics measured by the open-circuit method can yield an incorrect coupling coefficient k if the coil quality factor Q is low, i.e., if ωL / R (where ω is the measured angular frequency, L is the coil inductance, and R is the coil winding resistance) is small. The reason why an incorrect coupling coefficient k is calculated is explained below.
[0005] FIG. 8 shows a general equivalent circuit 900 of a transformer. The equivalent circuit 900 includes a primary winding resistance 901, a secondary winding resistance 902, a primary winding leakage inductance 903, a secondary winding leakage inductance 904, an excitation inductance 905, primary side terminals 906-a and 906-b, and secondary side terminals 907-a and 907-b. The magnitudes of the primary winding resistance 901 and the secondary winding resistance 902 are both R, the primary winding leakage inductance 903 and the secondary winding leakage inductance 904 are both (1-k)L, and the excitation inductance 905 is kL.
[0006] The impedance Z of the transformer as seen from the primary side terminals 906-a and 906-b when the secondary side terminals 907-a and 907-b are open open is given by Equation (2).
Equation
[0007] j is the imaginary unit. Since the coefficient of jω in Equation (2) is the inductance L when the secondary winding is open, Equation (3) is obtained. open is obtained.
Equation
[0008] The impedance Z of the transformer as seen from the primary side terminals 906-a and 906-b when the secondary side terminals 907-a and 907-b are short-circuited short is given by Equation (4).
Equation
[0009] When ωL / R in Equation (4) is replaced with the quality factor Q, Equation (5) is obtained.
Equation
[0010] In equation (4), when ωL / R >> 1, that is, when Q >> 1 in equation (5), Z short becomes equation (6).
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[0011] Since the coefficient of jω in equation (6) is the inductance L when the secondary winding is short - circuited in the case of ωL / R >> 1, that is, Q >> 1 short L short becomes equation (7).
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[0012] By eliminating L from equations (3) and (7), the calculation formula for the coupling coefficient k of the open - circuit short - circuit method shown in equation (1) is obtained.
[0013] However, when ωL / R → 0 in equation (4), that is, when Q → 0 in equation (5), Z short becomes equation (8).
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[0014] Since the coefficient of jω in equation (8) is the inductance L when the secondary winding is short - circuited in the case of ωL / R → 0, that is, Q → 0 short L short becomes equation (9).
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[0015] Substituting equations (3) and (9) into equation (1), the coupling coefficient k of the open - circuit short - circuit method becomes 0. The fact that the coupling coefficient k becomes 0 is an incorrect result that is completely inconsistent with reality. Generally, when a transformer has a primary winding N1, a secondary winding N2, and a coupling coefficient k, this is because equation (10) holds for the voltage ratio, which is the ratio of the secondary - side voltage V2 to the primary - side voltage V1.
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[0016] As explained above, an incorrect coupling coefficient k can be calculated when the coil quality coefficient Q is low. [Prior art documents] [Non-patent literature]
[0017] [Non-Patent Document 1] "JIS C5321 Test Methods for High-Frequency Coils and Intermediate-Frequency Transformers for Electronic Equipment," [online], [Accessed November 19, 2024], Internet <URL: https: / / kikakurui.com / c5 / C5321-1997-01.html> [Overview of the Initiative] [Problems that the invention aims to solve]
[0018] The objective of this invention is to accurately calculate the coupling coefficient when the quality coefficient of the coil is low. [Means for solving the problem]
[0019] One aspect of the present invention is a method for measuring coupling coefficients, comprising: a measurement step of measuring the current flowing through the primary winding, the voltage between the endpoints of the primary winding, and the voltage between the endpoints of the secondary winding when an alternating current is output to the primary winding of the transformer; and a calculation step of calculating the coupling coefficient of the transformer based on the voltage between the endpoints of the primary winding, the voltage between the endpoints of the secondary winding, the number of turns of the primary winding, and the number of turns of the secondary winding at the timing when the current becomes zero.
[0020] One aspect of the present invention is a coupling coefficient measurement system comprising: a measuring device that measures the current flowing through the primary winding of a transformer, the voltage between the endpoints of the primary winding, and the voltage between the endpoints of the secondary winding when an alternating current is output to the primary winding of the transformer; and a calculation device that calculates the coupling coefficient of the transformer based on the voltage between the endpoints of the primary winding, the voltage between the endpoints of the secondary winding, the number of turns of the primary winding, and the number of turns of the secondary winding at the timing when the current becomes zero.
[0021] One aspect of the present invention is a program that causes a computer to calculate the coupling coefficient of a transformer based on the voltage between the endpoints of the primary winding and the voltage between the endpoints of the secondary winding of the transformer, as well as the number of turns of the primary winding and the number of turns of the secondary winding, at the timing when the current flowing through the primary winding becomes zero when an alternating current is output to the primary winding of the transformer. [Effects of the Invention]
[0022] According to the present invention, it is possible to calculate an accurate coupling coefficient even when the quality coefficient of the coil is low. [Brief explanation of the drawing]
[0023] [Figure 1] This figure shows the configuration of the coupling coefficient measurement system 100 according to this embodiment. [Figure 2] This figure shows an example of the configuration of the measuring device 3. [Figure 3] This figure shows an example of the measurement results of voltage V1', voltage V2, and current IL, along with the timing τ. [Figure 4] This flowchart shows the procedure for calculating the frequency characteristics of the coupling coefficients. [Figure 5] This figure shows the specifications of transformer 1 used in the experiment and the measurement conditions. [Figure 6] This is an example of a measurement result. [Figure 7] This figure shows a comparison of the coupling coefficient k calculated in this embodiment and in the comparative example. [Figure 8] This is a typical equivalent circuit of a transformer, rated at 900. [Modes for carrying out the invention]
[0024] Embodiments of the present invention will be described in detail below with reference to the drawings. Figure 1 shows the configuration of the coupling coefficient measurement system 100 according to this embodiment. The coupling coefficient measurement system 100 comprises a signal generator 2, a measuring device 3, and a calculation device 4. The coupling coefficient measurement system 100 measures the coupling coefficient of the transformer 1.
[0025] Transformer 1 comprises a primary winding 11 and a secondary winding 12. The primary winding 11 has primary side terminals 111-a and 111-b at both ends. The secondary winding 12 has secondary side terminals 121-a and 121-b at both ends. The number of turns of the primary winding 11 is N1, and the number of turns of the secondary winding 12 is N2.
[0026] Signal generator 2 is connected to primary terminal 111-a. Primary terminal 111-b is grounded. Signal generator 2 outputs alternating current to primary terminal 111-a. This causes alternating current to flow through primary winding 11.
[0027] The measuring device 3 measures the voltage V1' between primary terminals 111-a and 111-b, the voltage V2 between secondary terminals 121-a and 121-b, and the magnitude I of the current flowing through the primary winding 11. L The measuring device 3 measures voltage V1', voltage V2, and current I for a period of more than half the period of the alternating current generated by the signal generator 2. L The following is measured. Figure 2 shows an example of the configuration of the measuring device 3. The measuring device 3 comprises a first differential voltage measuring instrument 31, a second differential voltage measuring instrument 32, a current measuring instrument 33, and an oscilloscope 34.
[0028] The first differential voltage measuring instrument 31 measures the voltage V1'. The first differential voltage measuring instrument 31 measures the voltage V1' by, for example, contacting two test pins with the primary terminals 111-a and 111-b, respectively.
[0029] The second differential voltage meter 32 measures the voltage V2. The second differential voltage meter 32 measures the voltage V2 by, for example, contacting two test pins with the secondary terminals 121-a and 121-b, respectively.
[0030] Current measuring instrument 33 measures current I L The current measuring instrument 33 is, for example, a clamp-type current sensor, and measures the current I connected to the primary winding 11. L By sandwiching the path through which current I flows, L The current measuring instrument 33 is a through-type current sensor and measures the current I connected to the primary winding 11. L By making the path through which the current flows pass through the hole in the center of the sensor, the current I L You may measure it.
[0031] The oscilloscope 34 measures voltage V1', voltage V2, and current I from the first differential voltage measuring instrument 31, the second differential voltage measuring instrument 32, and the current measuring instrument 33. L The measurement results are obtained. The oscilloscope 34 obtains the voltage V1', voltage V2, and current I for a period of more than half the period of the alternating current generated by the signal generator 2. L Obtain the measurement results.
[0032] The calculation unit 4 receives voltage V1', voltage V2, and current I from the measuring device 3. L The measurement results are obtained. The calculation unit 4 calculates the current I L Based on the voltages V1' and V2 at the timing when the value becomes 0, the coupling coefficient k of transformer 1 is calculated. More specifically, the calculation unit 4 calculates the coupling coefficient k of transformer 1 using equation (11).
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[0033] In equation (11), τ is the current I L This is the timing when the voltage becomes 0, V1'(τ) is the voltage V1' at τ, and V2(τ) is the voltage V2 at τ. Figure 3 shows the voltage V1', voltage V2, and current I LThis figure shows an example of measurement results and timing τ.
[0034] Equation (11) is derived from equation (10). Current I flows through the primary winding 11. L As a result of the current flow, the voltage V1' is, as shown in equation (12), the voltage drop V1 across the inductance of the primary winding 11 and the voltage drop V across the resistance of the primary winding 11. R It becomes the sum of these. Therefore, as shown in Figure 3, V1' is I L It is not in phase with V2.
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[0035] Furthermore, since no current flows through the secondary winding 12, there is no voltage drop due to the secondary winding resistance. Current I L When the value becomes 0, the voltage V R It also becomes 0. Therefore, the voltage V1'(τ) and the voltage V1(τ) at τ are equal. The calculation unit 4 determines the current I in the acquired measurement results. L If there are multiple timings where the coefficient is 0, the average value of the coupling coefficient k calculated based on voltages V1' and V2 at each timing may be calculated. This allows for the calculation of a coupling coefficient k with less variation.
[0036] While changing the frequency of the AC current output from the signal generator 2, the measuring device 3 measures voltage V1', voltage V2, and current I L By measuring the frequency and having the arithmetic unit 4 calculate the coupling coefficient k, the frequency characteristics of the coupling coefficient k can be calculated. The frequency of the AC current output from the signal generator 2 is changed, for example, after the arithmetic unit 4 has calculated the coupling coefficient k at a certain frequency. The frequency of the AC current output from the signal generator 2 may also be changed by manually operating the signal generator 2.
[0037] The arithmetic unit 4 outputs the frequency characteristics of the calculated coupling coefficient k of transformer 1. The arithmetic unit 4 displays the frequency characteristics of the calculated coupling coefficient k on a built-in display device, for example. The arithmetic unit 4 may also output the coupling coefficient k at a specific frequency. The arithmetic unit 4 may record the calculated coupling coefficient k of transformer 1 in its internal memory.
[0038] Figure 4 is a flowchart showing the procedure for calculating the frequency characteristics of the coupling coefficient. First, the signal generator 2 and measuring device 3 are connected to the transformer 1 (step S10). More specifically, one of the primary side terminals 111-a and 111-b of the primary winding 11 of the transformer 1 is connected to the signal generator 2, and the other terminal is grounded. The first differential voltage measuring instrument 31 is set to measure the voltage V1' between the primary side terminals 111-a and 111-b. The second differential voltage measuring instrument 32 is set to measure the voltage V2 between the secondary side terminals 121-a and 121-b. The current measuring instrument 33 measures the current I flowing through the primary winding 11. L Set it to measure.
[0039] Subsequently, the signal generator 2 starts outputting alternating current (step S11). The start of the alternating current output from the signal generator 2 may be controlled by the arithmetic unit 4, or it may be done by manually operating the signal generator 2.
[0040] The measuring device 3 measures the transformer 1 for a period of half a cycle or more of the alternating current (step S12). For example, the first differential voltage measuring instrument 31 measures the voltage V1' between the primary terminals 111-a and 111-b of the primary winding 11, the second differential voltage measuring instrument 32 measures the voltage V2 between the secondary terminals 121-a and 121-b of the secondary winding 12, and the current measuring instrument 33 measures the current I flowing through the primary winding 11. L Measure.
[0041] The calculation unit 4 calculates the coupling coefficient k based on the measurement results from the measuring device 3 (step S13). The calculation unit 4 calculates the current I L The coupling coefficient k is calculated based on the voltages V1'(τ) and V2(τ) at timing τ when the coefficient becomes 0.
[0042] Subsequently, if the coupling coefficients have not been calculated for all predetermined frequencies (step S14: NO), the calculation unit 4 changes the frequency of the AC current output from the signal generator 2 (step S15). Note that the frequency of the AC current output from the signal generator 2 may be changed by manually operating the signal generator 2. After the frequency of the AC current output from the signal generator 2 is changed, the measuring device 3 measures the transformer 1 in step S12, and the calculation unit 4 calculates the coupling coefficients in step S13.
[0043] If coupling coefficients have been calculated for all predetermined frequencies (Step S14: YES), the arithmetic unit 4 outputs the coupling coefficients calculated for each frequency (Step S16).
[0044] <experiment> The experiment conducted is described below. Figure 5 shows the specifications and measurement conditions of transformer 1 used in the experiment. The core material of transformer 1 is air-core, the number of turns N1 of the primary winding 11 is 18, the number of turns N2 of the secondary winding 12 is 18, the inductance L of the primary winding 11 is 17.5 μH, and the DC resistance R of the primary winding 11 is 341 mΩ. The signal output by signal generator 2 was a sine wave, and the frequencies of the output signal were 25 frequencies chosen to be logarithmically equally spaced from 1 kHz to 460 kHz. Current I L The maximum value was 1.0A.
[0045] Figure 6 shows an example of measurement results. Figure 6 shows the measurement results when the frequency of the signal output from signal generator 2 is 2.8 kHz. Current I L At timing τ1, where is 0, the voltage V1' was -0.315V and the voltage V2 was -0.0715V. Also, the current I L At timing τ2, where k is 0, the voltage V1' was 0.312V and the voltage V2 was 0.0710V. The coupling coefficient k at this time was calculated to be 0.23, expressed to two significant figures.
[0046] Similarly, the transformer 1 was measured and the coupling coefficient k was calculated when the signal generator 2 output signals of other frequencies. As a comparative example, the coupling coefficient k was also calculated using the open-circuit method described in JIS C5321. Figure 7 shows a comparison of the coupling coefficient k calculated in this embodiment and the comparative example. Figure 7 also shows the quality coefficient Q, which varies with frequency. The coupling coefficient k calculated in this embodiment remained almost constant at approximately 0.23 regardless of the quality coefficient Q. In contrast, the coupling coefficient k calculated in the comparative example was similar to this embodiment, ranging from 0.22 to 0.23 at frequencies above 30 kHz where the quality coefficient Q is 10 or higher. However, at frequencies below 30 kHz where the quality coefficient Q is 10 or lower, the coupling coefficient k decreased along with the quality coefficient Q, and at a frequency of 1 kHz, the coupling coefficient k was calculated to be 0.07. This value is completely inconsistent with the realistic coupling coefficient k of transformer 1. Therefore, in this embodiment, compared to the comparative example, it was possible to calculate an accurate coupling coefficient when the quality coefficient of the coil was low.
[0047] <Other Embodiments> Although one embodiment of this invention has been described in detail above with reference to the drawings, the specific configuration is not limited to that described above, and various design changes can be made without departing from the spirit of this invention.
[0048] The arithmetic unit 4 in the above-described embodiment may be implemented in whole or in part by a computer. In that case, the program for implementing this function may be recorded on a computer-readable recording medium, and the program recorded on this recording medium may be loaded into the computer system and executed. The term "computer system" here includes the OS and peripheral hardware. The term "computer-readable recording medium" refers to portable media such as flexible disks, magneto-optical disks, ROMs, CD-ROMs, and recording devices such as hard disks built into the computer system. Furthermore, the term "computer-readable recording medium" may also include those that dynamically hold programs for a short period of time, such as communication lines used when transmitting programs via networks such as the Internet or communication lines such as telephone lines, and those that hold programs for a certain period of time, such as volatile memory inside the computer system that acts as a server or client in such cases. The program may be for implementing a part of the functions described above, or it may be a program that can implement the functions described above in combination with a program already recorded in the computer system, or it may be implemented using a programmable logic device such as an FPGA (Field Programmable Gate Array). [Explanation of Symbols]
[0049] 100 Coupling coefficient measurement system, 1 Transformer, 11 Primary winding, 111-a, 111-b Primary terminals, 12 Secondary winding, 121-a, 121-b Secondary terminals, 2 Signal generator, 3 Measuring device, 31 First differential voltage meter, 32 Second differential voltage meter, 33 Current meter, 34 Oscilloscope, 4 Calculation unit, 900 Equivalent circuit, 901 Primary winding resistance, 902 Secondary winding resistance, 903 Primary winding leakage inductance, 904 Secondary winding leakage inductance, 905 Excitation inductance, 906-a, 906-b Primary terminals, 907-a, 907-b Secondary terminals
Claims
1. A measurement step that measures the current flowing through the primary winding, the voltage between the endpoints of the primary winding, and the voltage between the endpoints of the secondary winding when an alternating current is output to the primary winding of the transformer, A calculation step to calculate the coupling coefficient of the transformer based on the voltage between the endpoints of the primary winding at the timing when the current flowing through the primary winding becomes zero, the voltage between the endpoints of the secondary winding, the number of turns of the primary winding, and the number of turns of the secondary winding. A method for measuring the coupling coefficient.
2. The system includes a frequency changing step that changes the frequency of the AC current, In the measurement step described above, the current flowing through the primary winding, the voltage between the endpoints of the primary winding, and the voltage between the endpoints of the secondary winding are measured for each frequency. In the calculation step described above, the coupling coefficient is calculated for each frequency. The method for measuring the coupling coefficient according to claim 1.
3. In the measurement step, the voltage between the endpoints of the primary winding and the voltage between the endpoints of the secondary winding are measured at multiple timings when the current is zero. In the calculation step described above, the average value of the coupling coefficients calculated based on the voltages between the endpoints of the primary winding and the voltages between the endpoints of the secondary winding at multiple timings where the current is zero is calculated as the coupling coefficient of the transformer. A method for measuring the coupling coefficient according to claim 1 or 2.
4. A measuring device for measuring the current flowing through the primary winding of a transformer, the voltage between the endpoints of the primary winding, and the voltage between the endpoints of the secondary winding when an alternating current is output to the primary winding of the transformer, A calculation device that calculates the coupling coefficient of the transformer based on the voltage between the endpoints of the primary winding at the timing when the current flowing through the primary winding becomes zero, the voltage between the endpoints of the secondary winding, the number of turns of the primary winding, and the number of turns of the secondary winding. A system for measuring coupling coefficients, equipped with the following features.
5. When an alternating current is output to the primary winding of the transformer, the computer calculates the coupling coefficient of the transformer based on the voltage between the endpoints of the primary winding and the voltage between the endpoints of the secondary winding of the transformer, as well as the number of turns of the primary winding and the number of turns of the secondary winding, at the timing when the current flowing through the primary winding becomes zero. program.