A switched-current sampling circuit and a sampling method
By using PCB metal foil instead of sampling resistors in switching power supplies, data is collected in combination with voltage and temperature to calculate sampling current, the accuracy problems of sampling resistors and large space occupation are solved, and high-precision and space-saving current sampling is achieved.
Patent Information
- Application Number
- CN202210200456.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-03-02
- Publication Date
- 2025-06-20
- Estimated Expiration
- 2042-03-02
AI Technical Summary
The use of sampling resistors for current sampling in existing switching power supplies has accuracy problems, requires additional space and increases production costs, and the excessive heating power of the sampling resistors leads to an increase in space occupation.
The PCB metal foil that already exists in the switching power supply circuit is used to sample the current instead of the separately set sampling resistor. By collecting the voltage and temperature of the metal foil, the sampling current is calculated using the pre-obtained fitting curve and proportional relationship.
No additional sampling resistance is required, space saving, improve PCB design flexibility, eliminate the impact of temperature on sampling accuracy, and improve the reliability and accuracy of current sampling.
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Figure CN114594301B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of AC-DC power supplies, and particularly relates to a switching current sampling circuit and a sampling method. Background Art
[0002] Switching power supplies usually need to perform current sampling as feedback or control signals. Currently, most current sampling methods use sampling resistors for current sampling. The sampling resistor is connected in series in the circuit, and by collecting the voltage across the sampling resistor and applying Ohm's law I = U / R, the voltage is converted into current.
[0003] However, there are generally the following problems in using sampling resistors for current sampling:
[0004] (1) One or more additional current sampling resistors are required;
[0005] (2) The resistor manufacturing process will introduce errors, resulting in accuracy problems in current sampling all the time. Improving accuracy often requires increasing production costs;
[0006] (3) When selecting a sampling resistor, the self-heating power of the resistor needs to be considered under the requirement of reliability. When the heating power is too large, a high-power sampling resistor needs to be used, which will increase the volume of the resistor device, occupy a large space in the switching power supply, and increase the difficulty of PCB layout for some applications with limited space requirements. Summary of the Invention
[0007] To solve the above problems, the present invention proposes a switching current sampling circuit and a sampling method, which use the PCB metal foil already existing in the switching circuit to replace the separately provided sampling resistor for current sampling, meeting the functional implementation and accuracy requirements of current sampling.
[0008] The first aspect of the present invention is to provide a switching current sampling circuit, including a metal foil in a switching power supply circuit and an acquisition and processing unit;
[0009] The metal foil is a component of the circuit through which the sampling current flows;
[0010] The acquisition and processing unit is used to collect the voltage and temperature of the metal foil when the sampling current flows through the metal foil, and obtain the sampling current according to the voltage and temperature of the metal foil.
[0011] As an implementation manner, the method for obtaining the sampling current is: according to the fitting curve of the voltage and current at the reference temperature t0 of the metal foil obtained in advance, and the proportional relationship between the voltage at different temperatures and the voltage at the reference temperature t0, combined with the currently collected voltage and temperature of the metal foil, determine the current sampling current.
[0012] As an implementation manner, the process of obtaining the fitting curve of the voltage and current at the reference temperature t0 is as follows: Set the reference temperature t0, and while maintaining the reference temperature t0, inject currents I1, I2, …, I n into the metal foil respectively, and measure the voltage values of the metal foil corresponding to the respective currents. According to the obtained voltage and current values of the metal foil, fit the curve of the voltage of the metal foil corresponding to the current at the reference temperature t0.
[0013] As an implementation manner, the process of obtaining the proportional relationship between the voltages at different temperatures and the voltage at the reference temperature t0 is as follows: At different temperatures, collect the voltage of the metal foil and the actual temperature of the metal foil based on a fixed current value, and take the voltage at the reference temperature t0 as the standard to obtain the proportional relationship between the voltage of the metal foil at different temperatures and the voltage at the reference temperature t0 respectively.
[0014] As an implementation manner, the metal foil is at least part of the printed circuit on the PCB board in the switching power supply.
[0015] As an implementation manner, the metal foil is at least part of the copper foil on the PCB board in the switching power supply.
[0016] As an implementation manner, the acquisition and processing unit includes a control module, a sampling module, a differential amplification module, a digital-to-analog conversion module, a compensation module, and a display module;
[0017] The control module is used to control the operation of each module in the acquisition and processing unit;
[0018] The sampling module is used to collect the voltage and temperature of the metal foil through which the sampling current flows;
[0019] The differential amplification module is used to amplify the voltage collected by the sampling module;
[0020] The digital-to-analog conversion module is used to perform digital-to-analog conversion on the voltage amplified by the differential amplification module;
[0021] The compensation module is used to perform compensation calculation on the digital value of the voltage after digital-to-analog conversion to obtain the current sampling current value;
[0022] The display module is used to display the current sampling current value.
[0023] As an implementation manner, the resistivity of the metal foil is proportional to the temperature.
[0024] As an implementation manner, when the metal foil is copper foil and the reference temperature t0 is set to 20 °C, the relationship between the voltage U and current I of the copper foil is:
[0025] The voltage ratio relationships of the copper foil at different temperatures to the voltage at the reference temperature of 20°C are respectively as follows:
[0026]
[0027] Among them, K n respectively represents the voltage ratio of the copper foil at temperature n to the voltage at the reference temperature of 20°C, and U n respectively represents the voltage of the copper foil at temperature n.
[0028] The second aspect of the present invention is to provide a switching power supply current sampling method, including a metal foil in the switching power supply circuit and an acquisition and processing unit;
[0029] The metal foil is a component of the circuit through which the sampling current flows;
[0030] The acquisition and processing unit is used to acquire the voltage and temperature of the metal foil when the sampling current flows through the metal foil, and obtain the sampling current according to the voltage and temperature of the metal foil.
[0031] As an implementation manner, the method for determining the sampling current is: the method for obtaining the sampling current is: according to the fitting curve of the voltage and current of the metal foil at the reference temperature t0 obtained in advance, and the voltage ratio relationship at different temperatures to the voltage at the reference temperature, combined with the currently acquired voltage and temperature of the metal foil, determine the current sampling current.
[0032] As an implementation manner, the process of obtaining the fitting curve of the voltage and current at the reference temperature t0 is to set the reference temperature t0, and while maintaining the reference temperature t0, inject currents I1, I2,..., I n into the metal foil respectively, and measure the voltage values of the metal foil corresponding to the respective currents, and fit a curve of the voltage of the metal foil corresponding to the current at the reference temperature t0 according to the obtained voltage and current values of the metal foil.
[0033] As an implementation manner, the process of obtaining the voltage ratio relationship at different temperatures to the voltage at the reference temperature t0 is: First, collect the voltage of the metal foil and the actual temperature of the metal foil at different temperatures based on a fixed current value, and take the voltage at the reference temperature t0 as the standard to obtain the voltage ratio relationships of the metal foil at different temperatures to the voltage at the reference temperature t0 respectively.
[0034] As an implementation manner, the process of determining the current sampling current is:
[0035] Based on the temperature and voltage values of the currently collected metal foil, and combining with the obtained proportional relationship between the voltage at different temperatures and the voltage at the reference temperature t0, determine the voltage of the metal foil at the reference temperature t0. Then, according to the fitting curve of the voltage and current of the metal foil at the reference temperature t0, determine the current sampled by the metal foil at present.
[0036] As an implementation manner, when the metal foil is a copper foil and the reference temperature t0 is set to 20 °C, the relationship between the voltage U and current I of the copper foil is:
[0037] The proportional relationships between the copper foil voltages at different temperatures and the voltage at the reference temperature of 20 °C are respectively:
[0038]
[0039] where K n respectively represents the ratio of the copper foil voltage at temperature n to the copper foil voltage at the reference temperature of 20 °C, and U n respectively represents the copper foil voltage at temperature n.
[0040] Compared with the prior art, the remarkable advantages and beneficial effects of the present invention are as follows:
[0041] (1) The current sampling circuit proposed by the present invention no longer requires adding an additional sampling resistor in the switching power supply circuit. The sampling metal foil itself is a part of the switching power supply circuit, saving space and improving the difficulty of PCB layout.
[0042] (2) The current sampling circuit proposed by the present invention utilizes the metal foil existing in the switching power supply circuit itself, utilizes the characteristic that its resistivity is proportional to temperature, and utilizes the proportional relationship between the voltages at different temperatures to eliminate the influence of temperature on the resistance of the metal foil, and obtains a stable result that does not change with temperature.
[0043] (3) The current sampling circuit proposed by the present invention utilizes the tolerance temperature of a specific metal itself and the area of the metal foil being several times that of the sampling resistor after being processed into a metal foil. If the same current flows through, in the same heat dissipation environment, the temperature rise brought by the metal foil is much smaller than that of the resistor, greatly reducing the influence brought by its own heat generation and improving the reliability of current sampling.
[0044] Other features and advantages of the present invention will be described in the subsequent specification, and part of them will be obvious from the specification, or can be understood by implementing the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the structures specifically pointed out in the written specification, claims, and drawings. Brief Description of the Drawings
[0045] The accompanying drawings are only for the purpose of illustrating specific embodiments and are not considered to be a limitation of the present invention. Throughout the drawings, the same reference signs denote the same components.
[0046] Figure 1 It is a schematic diagram of the switching current sampling circuit structure in Embodiment 1.
[0047] Figure 2 It is the fitting curve of copper foil current and voltage in Embodiment 1.
[0048] Figure 3 It is a schematic diagram of the processing flow of the acquisition and processing unit in Embodiment 1.
[0049] Figure 4 It is a flowchart of the steps of the switching power supply current sampling method in Embodiment 2. Specific Embodiments
[0050] It is easily understood that according to the technical solution of the present invention, without changing the essence of the present invention, those of ordinary skill in the art can imagine various embodiments of the present invention. Therefore, the following specific embodiments and drawings are only illustrative descriptions of the technical solution of the present invention and should not be regarded as all of the present invention or as a limitation or restriction of the technical solution of the present invention. On the contrary, the purpose of providing these embodiments is to enable those skilled in the art to more thoroughly understand the present invention. The preferred embodiments of the present invention will be specifically described below with reference to the accompanying drawings, in which the drawings form a part of this application and are used together with the embodiments of the present invention to illustrate the innovative concept of the present invention.
[0051] Embodiment 1
[0052] As Figure 1 shown, the switching current sampling circuit in this embodiment includes the metal foil in the switching power supply circuit and the acquisition and processing unit;
[0053] Among them, the metal foil is a part of the circuit through which the sampling current flows. Specifically, the metal foil in the switching power supply circuit in this embodiment uses a copper foil, which is a part of the copper foil with current flowing in the main power loop of the PCB board itself in the switching power supply circuit. Theoretically, the selection of this copper foil does not need to consider the length and size of the copper foil.
[0054] The acquisition and processing unit is used to acquire the voltage and temperature of the metal foil when the sampling current flows through the metal foil, and obtain the sampling current according to the voltage and temperature of the metal foil.
[0055] When using the metal foil as a resistor, the calculation formula for its resistance value is:
[0056]
[0057] Among them, ρ represents the resistivity of the metal foil, L represents the length of the metal foil, and S represents the cross-sectional area of the metal foil;
[0058] When the resistivity of the metal foil is proportional to the temperature, the relationship between the resistivity of the metal foil and the temperature is:
[0059]
[0060] Among them, t0 represents the set reference temperature, ρ t0 represents the resistivity of the metal at the reference temperature, T represents the actual temperature, and n represents the correction coefficient of the metal.
[0061] It can be seen that when the length and cross-sectional area of the metal foil are determined, the change in its resistance value is only related to the temperature. Therefore, by using this characteristic to sample multiple times, the proportional value relationship of the voltage at different temperatures is obtained, and the proportional factor of the resistivity between the copper foils at different temperatures is eliminated.
[0062] According to the fitting curve of the voltage and current of the metal foil at the reference temperature t0 obtained in advance, and the proportional relationship between the voltage at different temperatures and the voltage at the reference temperature t0, combined with the currently collected voltage and temperature of the metal foil, the current of the current sampling is determined.
[0063] Among them, the process of obtaining the fitting curve of the voltage and current at the reference temperature t0 is to set the reference temperature t0, and while maintaining the reference temperature t0, inject currents I1, I2,..., I n into the metal foil respectively, and measure the voltage values of the metal foil corresponding to the respective currents. According to the relationship between the voltage and current of the obtained metal foil, a curve of the voltage of the metal foil corresponding to the current at the reference temperature t0 is fitted.
[0064] In this embodiment, the reference temperature is set to 20 °C. Then, the resistivity of the copper foil at the actual temperature T is:
[0065]
[0066] Place the switching current sampling circuit using copper as the metal foil in this embodiment in a constant temperature environment of 20 °C, and use a fan for auxiliary heat dissipation to keep the surface temperature of the copper foil at 20 °C. Then, inject a series of known currents and measure the voltage values of the copper foil to obtain the copper foil current and voltage in the following table:
[0067] I / A U / V 10A 0.47V 20A 0.75V 30A 1.03V 40A 1.31V 50A 1.59V
[0068] According to the current values and voltage values of the copper foil in the above table, fit the relationship curve between the current and voltage on the copper foil, as Figure 2 shown, that is:
[0069] U = 0.028I + 0.19
[0070]
[0071] Subsequently, based on a fixed current value I0 = 20 A, the copper foil voltage and the actual temperature of the copper foil were collected at different temperatures, and the temperature and voltage of the copper foil at I0 = 20 A in the following table were obtained:
[0072] T / ℃ U / V 10℃ 0.717V 20℃ 0.750V 30℃ 0.781V 40℃ 0.813V 50℃ 0.846V
[0073] Combining the above table, the proportional relationship between the copper foil voltage at different temperatures and the copper foil voltage at 20°C can be obtained:
[0074]
[0075] And taking the voltage at the reference temperature t0 as the standard, the proportional relationship between the copper foil voltage at different temperatures and the voltage at the reference temperature t0 was obtained respectively.
[0076] According to the obtained proportional relationship, the voltage corresponding to different temperatures at 20°C can be known:
[0077]
[0078] Then, according to the relationship curve between the current and voltage on the copper foil the corresponding current values at different temperatures can be determined:
[0079]
[0080]
[0081] Utilizing the characteristic that the resistivity of the copper foil is proportional to the temperature, through multiple samplings, the proportional value relationship of the voltage at different temperatures was obtained, eliminating the proportional factor of the resistivity between copper foils at different temperatures, thereby obtaining a stable result that does not change with temperature;
[0082] It should be further noted that all metals with resistivity proportional to temperature can be applied to the switching current sampling circuit of the present invention.
[0083] It can be seen from the results that the calculated value of the current compensation at different temperatures using this sampling circuit is almost equal to the actually injected current, and the measurement error is very small and the accuracy is very high.
[0084] Furthermore, as Figure 3 shown, the acquisition and processing unit in the current sampling circuit includes a control module, a sampling module, a differential amplification module, a digital-to-analog conversion module, a compensation module, and a display module;
[0085] Among them, the sampling module collects the temperature and voltage of the copper foil in the switching power supply circuit, and sends the voltage to the differential amplification module for amplification. The amplified voltage value is sent to the analog-to-digital conversion module to complete analog-to-digital conversion. The compensation module performs compensation calculation on the voltage digital value after analog-to-digital conversion, so as to obtain the current sampling current value and send it to the display module for display.
[0086] Embodiment 2
[0087] As Figure 4 shown, a switching power supply current sampling method provided by this embodiment includes the following steps:
[0088] S1. When the sampling current flows through, the acquisition and processing unit acquires the voltage and temperature of the metal foil in the switching power supply circuit;
[0089] S2. The acquisition and processing unit determines the current sampling current by combining the voltage and temperature of the metal foil collected in S1 with the fitting curve of the voltage and current of the metal foil at the reference temperature t0 and the proportional relationship between the voltages at different temperatures and the voltage at the reference temperature t0 obtained in advance.
[0090] Among them, the method for obtaining the fitting curve of the voltage and current of the metal foil at the reference temperature is to set the reference temperature t0, and while maintaining the reference temperature t0, inject currents I1, I2,..., I n into the metal foil respectively, and measure the voltage values of the metal foil corresponding to the respective currents. According to the obtained voltage and current values of the metal foil, the curve of the voltage of the metal foil corresponding to the current at the reference temperature t0 is fitted.
[0091] Among them, the process of obtaining the proportional relationship between the voltages at different temperatures and the voltage at the reference temperature t0 is as follows: at different temperatures, the voltage of the metal foil and the actual temperature of the metal foil are collected based on a fixed current value, and taking the voltage at the reference temperature t0 as the standard, the proportional relationship between the voltages of the metal foil at different temperatures and the voltage at the reference temperature t0 is obtained respectively.
[0092] Specifically, the acquisition and processing unit in S1 includes a control module, a sampling module, a differential amplification module, an analog-to-digital conversion module, a compensation module, and a display module;
[0093] Among them, the sampling module is used to collect the temperature and voltage of the metal foil in the switching power supply circuit, and send the voltage to the differential amplification module for amplification. The amplified voltage value is sent to the analog-to-digital conversion module to complete analog-to-digital conversion. The compensation module performs compensation calculation on the voltage digital value after analog-to-digital conversion, so as to obtain the current sampling current value and send it to the display module for display.
[0094] The present invention uses the PCB metal foil already existing in the circuit for current sampling, replacing the traditional sampling resistor sampling method, reducing the sampling devices, optimizing the design space of the PCB. At the same time, the sampling error caused by the temperature change of the metal foil itself is eliminated through compensation algorithm optimization, achieving the desired design accuracy, greatly saving the production cost and improving the production efficiency.
[0095] As described above, only the preferred specific embodiments of the present invention are given, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.
[0096] It should be understood that, in order to streamline the present invention and help those skilled in the art understand various aspects of the present invention, in the above description of the exemplary embodiments of the present invention, various features of the present invention are sometimes described in a single embodiment or with reference to a single figure. However, the present invention should not be construed as meaning that the features included in the exemplary embodiments are all essential technical features of the claims of this patent.
[0097] Those skilled in the art can understand that all or part of the processes for implementing the methods of the above embodiments can be completed by instructing relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. Among them, the computer-readable storage medium is a disk, an optical disc, a read-only memory or a random access memory, etc.
[0098] It should be understood that the modules, units, components, etc. included in the device of an embodiment of the present invention can be adaptively changed to be arranged in a device different from that of this embodiment. The different modules, units or components included in the device of the embodiment can be combined into one module, unit or component, or they can be divided into multiple sub-modules, sub-units or sub-components.
[0099] The modules, units or components in the embodiments of the present invention can be implemented in hardware, or in software running on one or more processors, or in a combination thereof. Those skilled in the art should understand that a microprocessor or a digital signal processor (DSP) can be used in practice to implement the embodiments of the present invention. The present invention can also be implemented as a computer program product or a computer-readable medium for executing part or all of the methods described herein.
Claims
1. A switched-current sampling circuit, characterized in that, It includes a metal foil in a switching power supply circuit and an acquisition and processing unit; The metal foil is a component of the circuit through which the sampled current flows; The acquisition and processing unit is used to acquire the voltage and temperature of the metal foil when the sampled current flows through the metal foil, and obtain the sampled current according to the voltage and temperature of the metal foil; The method for obtaining the sampled current is as follows: according to the fitting curve of the voltage and current of the metal foil at the reference temperature t0 obtained in advance, and the proportional relationship between the voltages at different temperatures and the voltage at the reference temperature t0, combined with the currently acquired voltage and temperature of the metal foil, determine the current sampled current; The process of obtaining the fitting curve of voltage and current at the reference temperature t0 is as follows: Set the reference temperature t0, and while maintaining the reference temperature t0, inject currents I1, I2, …, I n into the metal foil respectively, and measure the voltage values of the metal foil corresponding to the respective currents. According to the obtained voltage and current values of the metal foil, fit the curve of the voltage of the metal foil corresponding to the current at the reference temperature t0; The process of obtaining the proportional relationship between the voltages at different temperatures and the voltage at the reference temperature t0 is as follows: at different temperatures, collect the voltage of the metal foil and the actual temperature of the metal foil based on a fixed current value, and take the voltage at the reference temperature t0 as the standard to obtain the proportional relationship between the voltage of the metal foil at different temperatures and the voltage at the reference temperature t0 respectively; The process of determining the current sampled current is as follows: According to the currently acquired temperature and voltage values of the metal foil, combined with the obtained proportional relationship between the voltages at different temperatures and the voltage at the reference temperature t0, determine the voltage of the metal foil at the reference temperature t0, and then according to the fitting curve of the voltage and current of the metal foil at the reference temperature t0, determine the current sampled current of the metal foil.
2. The switched-current sampling circuit according to claim 1, characterized in that, The metal foil is at least part of the printed circuit in the PCB board of the switching power supply.
3. The switched-current sampling circuit according to claim 1, characterized in that, The metal foil is at least part of the copper foil in the PCB board of the switching power supply.
4. The switched-current sampling circuit according to claim 1, characterized in that, The acquisition and processing unit includes a control module, a sampling module, a differential amplification module, a digital-to-analog conversion module, a compensation module, and a display module; The control module is used to control the operation of each module in the acquisition and processing unit; The sampling module is used to acquire the voltage and temperature of the metal foil through which the sampled current flows; The differential amplification module is used to amplify the voltage acquired by the sampling module; The digital-to-analog conversion module is used to perform digital-to-analog conversion on the voltage amplified by the differential amplification module; The compensation module is used to perform compensation calculation on the digital value of the voltage after digital-to-analog conversion to obtain the current sampled current value; The display module is used to display the current sampled current value.
5. The switched-current sampling circuit according to claim 1, characterized in that, The resistivity of the metal foil is proportional to the temperature.
6. The switched-current sampling circuit according to claim 1, characterized in that, When the metal foil is a copper foil and the reference temperature t0 is set to 20 °C, the relationship between the voltage U and current I of the copper foil is: The proportional relationships between the copper foil voltages at different temperatures and the voltage at the reference temperature of 20 °C are respectively: Among them, K n respectively represents the voltage ratio of the copper foil at temperature n to the voltage at the reference temperature of 20°C, and U n respectively represents the copper foil voltage at temperature n.
7. A switched-mode power supply current sampling method, characterized in that, It includes a metal foil in a switching power supply circuit and an acquisition and processing unit; The metal foil is a component of the circuit through which the sampled current flows; The acquisition and processing unit is used to acquire the voltage and temperature of the metal foil when the sampled current flows through the metal foil, and obtain the sampled current according to the voltage and temperature of the metal foil; The method for obtaining the sampled current is as follows: according to the fitting curve of the voltage and current of the metal foil at the reference temperature t0 obtained in advance, and the proportional relationship between the voltages at different temperatures and the voltage at the reference temperature, combined with the currently acquired voltage and temperature of the metal foil, determine the current sampled current; The process of obtaining the fitting curve of voltage and current at the reference temperature t0 is as follows: set the reference temperature t0, and while maintaining the reference temperature t0, inject currents I1, I2, …, I n into the metal foil respectively, and measure the voltage values of the metal foil corresponding to the respective currents. According to the obtained voltage and current values of the metal foil, fit a curve of the voltage of the metal foil corresponding to the current at the reference temperature t0; The process of obtaining the proportional relationship between the voltages at different temperatures and the voltage at the reference temperature t0 is as follows: First, at different temperatures, the voltage of the metal foil and the actual temperature of the metal foil are collected based on a fixed current value, and taking the voltage at the reference temperature t0 as the standard, the proportional relationships between the voltages of the metal foil at different temperatures and the voltage at the reference temperature t0 are obtained respectively; The process of determining the current sampling current is as follows: According to the temperature and voltage values of the metal foil collected currently, combined with the obtained proportional relationships between the voltages at different temperatures and the voltage at the reference temperature t0, the voltage of the metal foil at the reference temperature t0 is determined, and then according to the fitting curve of the voltage and current of the metal foil at the reference temperature t0, the current sampling current of the metal foil is determined.
8. The switching power supply current sampling method according to claim 7, wherein, When the metal foil is a copper foil and the reference temperature t0 is set to 20 °C, the relationship between the voltage U and the current I of the copper foil is: The proportional relationships between the copper foil voltages at different temperatures and the voltage at the reference temperature of 20 °C are respectively: Among them, K n respectively represent the ratio of the copper foil voltage at temperature n to the voltage at the reference temperature of 20°C, and U n respectively represent the copper foil voltage at temperature n.
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