Thermoelectric power generation module and biological position detection system
By employing ultra-small thermoelectric elements with a large aspect ratio and a highly heat-dissipative flexible sheet, the thermoelectric power generation module effectively addresses the challenge of generating sufficient power for advanced wearable biosensing devices with small temperature differences and limited surface areas.
Patent Information
- Application Number
- JP2022518592
- Authority / Receiving Office
- JP · JP
- Patent Type
- Patents
- Current Assignee / Owner
- Priority Date
- 2020-05-01
- Filing Date
- 2020-11-05
- Publication Date
- 2025-06-13
- Estimated Expiration
- 2040-11-05
AI Technical Summary
Existing thermoelectric power generation modules for wearable devices struggle to generate sufficient power with small temperature differences and limited surface areas, making them unsuitable for driving advanced biosensing devices with communication functions.
The development of a thermoelectric power generation module with ultra-small thermoelectric elements having a large aspect ratio, mounted at high density on flexible printed circuit boards, and enhanced with a highly heat-dissipative flexible sheet to increase the temperature difference across the module.
This solution enables the generation of 60 mV and 75 μW at a 1°C temperature difference, sufficient to power a wearable biosensing device, and can be scaled to meet the power requirements of more advanced devices.
Smart Images

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Abstract
Description
Technical Field
[0001] The present invention relates to a thermoelectric power generation module that adheres to a living body and generates electricity and is driven by the heat of the living body, and a wearable biosensing device and a living body position detection system using the same.
Background Art
[0002] Due to the importance of preventive medicine, research and development of wearable devices that can always adhere to a living body, sense, manage, and communicate medical data of the living body, and also notify the position information of the living body is active. In order to always adhere to the living body, it is essential to thoroughly miniaturize and power-save the device. At the same time, it is necessary to make the power source that drives the device wearable.
[0003] As a power source for driving wearable devices, small batteries have mainly been studied conventionally. However, the battery replacement cost is a major issue, and there is a strong demand for the development of a self-powered source by thermoelectric power generation that utilizes the heat of the living body.
[0004] As such a wearable thermoelectric power generation device, Non-Patent Document 1 discloses a wearable device for a wristwatch that can operate with slight thermoelectric power generation by a living body. This wearable device is a thermoelectric power generation unit in which 10 minute thermoelectric elements having a length of 80 μm, a width of 80 μm, and a height of 600 μm are densely mounted on two Si substrates having a length of 2 mm, a width of 2 mm, and a thickness of 300 μm by an advanced mounting technique, and the units are connected in series to generate electricity and drive the wristwatch.
[0005] However, since this wearable device is densely mounted by an advanced mounting technique, in addition to being costly, the generated power is 3 mV / cm 2 and 1 μW / cm 2 and the power generation power per unit area is small, and it cannot be used for a more advanced biosensing device having a communication function or the like.
[0006] The applicant of the present application has disclosed in Patent Document 1 a highly efficient flexible thermoelectric power generation module that can efficiently generate electricity from a low-temperature waste heat source. FIG. 11 is a cross-sectional view showing the configuration of the flexible thermoelectric power generation module disclosed in Patent Document 1. As shown in FIG. 11, the thermoelectric power generation module has a structure in which a plurality of thermoelectric elements 102 are densely mounted on a flexible printed circuit board 101, and a flexible printed circuit board 103 disposed on the thermoelectric elements 102, and the thermoelectric elements 102 are connected by wiring. Further, a slit 104 is formed in the flexible printed circuit board 103, whereby the thermoelectric power generation module can be freely bent. As a result, the thermoelectric power generation module can be mounted on a heat source having a curved surface with good adhesion.
[0007] Since this thermoelectric power generation module can be attached to a living body to generate electricity, it can achieve a high power generation efficiency compared to a self-powered power source for wearable devices by conventional thermoelectric power generation. However, for an advanced wearable biosensing device having a communication function or the like, power generation with a slight temperature difference and a small area is required. Even with this thermoelectric power generation module, there has been a problem that the generated voltage and generated power per unit area are too small to be used as they are.
Prior Art Documents
Patent Documents
[0008]
Patent Document 1
Non-Patent Documents
[0009]
Non-Patent Document 1
Summary of the Invention
Problems to be Solved by the Invention
[0010] In thermoelectric power generation, the greater the temperature difference between both ends of the thermoelectric power generation module, the greater the power generation amount can be. However, when the thermoelectric power generation module is constantly in close contact with a living body for power generation, even if the thermoelectric power generation module is composed of thermoelectric elements with a large aspect ratio in order to increase the thermal resistance of the thermoelectric power generation module, for example, when the temperature of the living body as the heat source is 35 °C and the outside air temperature is 30 °C, the temperature difference that can be ensured between both ends of the thermoelectric power generation module is at most about 1 °C exceeding.
[0011] However, in order to drive an advanced wearable biosensing device having functions such as sensing, management, and communication functions of medical data of a living body, with this temperature difference of only about 1 °C and a thermoelectric power generation module with a small area of about 5 cm × 2.5 cm essential for wearables, at least 100 mV (8 mV / cm 2 ) of operating voltage and 100 μW (8 μW / cm 2 ) of power generation power are required.
[0012] In order to generate the power required to drive a wearable device with a small temperature difference of about 1 °C and a thermoelectric power generation module with a small area, it is necessary to miniaturize the thermoelectric elements, make them slender to increase the aspect ratio, connect a large number in series within a small area, and perform high-density mounting.
[0013] According to experiments, even for thermoelectric elements made of BiTe-based thermoelectric materials with excellent thermoelectric conversion efficiency, for example, in order to obtain a power generation power of 100 mV and 100 μW with a temperature difference of 1 °C, thermoelectric elements with a width of 1 mm, a length of 1 mm, and a height of 1.5 mm are required to be at least 1000, that is, 500 pairs of p-type and n-type thermoelectric element pairs (pn pairs) are connected in series. Also, for wearable devices, since it is necessary to make the size of the thermoelectric power generation module at least 2.5 cm × 5.0 cm or less, a high-density mounting of 80 (40 pairs of pn pairs) / cm 2 or more is required.
[0014] However, generally, since thermoelectric elements are brittle and easily broken, when the chip size of the thermoelectric element becomes small, it becomes difficult to handle the thermoelectric element during mounting. Therefore, a large number of thermoelectric elements necessary to generate a practical electromotive force with a minute temperature difference of about 1 °C, for example, 50 pieces (25 pairs of pn junctions) / cm 2 or more, have not been mounted on a flexible printed circuit board at such a high density until now.
[0015] In addition, in thermoelectric power generation, the greater the temperature difference between both ends of the thermoelectric power generation module, the greater the amount of power generation that can be achieved. Therefore, in a thermoelectric power generation module, in order to reduce the thermal resistance between the module and the outside air, usually, an air-cooled heat sink or a water-cooled cooler or the like is closely attached to the low-temperature side to make the temperature difference between both ends of the module as large as possible. However, in a wearable thermoelectric power generation module that generates power using the temperature difference between body temperature and outside air temperature, it has been difficult to increase the temperature difference because a large cooler cannot be installed on the outside air side.
[0016] The present invention has been made in view of such problems, and its main object is to enable high-density mounting of ultra-small thermoelectric elements with a large aspect ratio on a flexible printed circuit board, and to provide a thermoelectric power generation module that can drive a highly functional wearable biosensing device even with a small temperature difference in an ultra-small size.
[0017] In addition, even when the thermoelectric power generation module is closely attached to a living body to generate power, it is an object of the present invention to provide a thermoelectric power generation module capable of creating a temperature difference of 1 °C or more between both ends of the thermoelectric power generation module.
Means for Solving the Problems
[0018] The thermoelectric power generation module according to the present invention is a thermoelectric power generation module in which a plurality of p-type thermoelectric elements and n-type thermoelectric elements are alternately connected in series and sandwiched and mounted on first and second flexible printed circuit boards, wherein the p-type thermoelectric elements and the n-type thermoelectric elements have a chip size of 1 mm or less and 0.2 mm or more, and a height of 0.8 mm or more and 3 mm or less.
[0019] In a preferred embodiment, the p-type thermoelectric element and the n-type thermoelectric element are cylinders with an aspect ratio (height of the cylinder / diameter of the bottom circle) of 1.5 or more, and the mounting density of each thermoelectric element of the p-type thermoelectric element and the n-type thermoelectric element is 1 cm 2 has 80 or more per.
Advantages of the Invention
[0020] According to the present invention, it is possible to provide a thermoelectric power generation module that enables high-density mounting of thermoelectric elements that are ultra-small and have a large aspect ratio, and can drive a highly functional wearable biosensing device even with an ultra-small temperature difference.
[0021] In addition, even when the thermoelectric power generation module is closely attached to the living body to generate electricity, it is possible to provide a thermoelectric power generation module capable of creating a temperature difference of 1°C or more between both ends of the thermoelectric power generation module.
Brief Description of the Drawings
[0022]
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Figure 11
Mode for Carrying Out the Invention
[0023] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. Note that the present invention is not limited to the following embodiments, and can be appropriately modified without departing from the scope in which the effects of the present invention are achieved.
[0024] Figure 1 is a graph showing the calculated number of mountable thermoelectric elements per 1 cm 2 with respect to the chip size of the thermoelectric element. Here, the chip size is defined as the diameter in the case of a cylindrical thermoelectric element, and the length of one side (in the case where the lengths of two sides are different, the average value) in the case of a rectangular prism. In addition, in order to mount the thermoelectric elements as densely as possible, the distance between chips is extremely narrowed to 0.1 mm.
[0025] As shown in Figure 1, when the chip size is 1 mm, about 80 thermoelectric elements can be mounted per 1 cm 2 and when the chip size is 1 mm or less, the number of mountable elements increases significantly. Therefore, by making the chip size 1 mm or less, it becomes possible to densely mount a large number of thermoelectric elements required for driving a wearable device. On the other hand, if the chip size becomes too small, the robustness of the chip is impaired, so the chip size is preferably 0.2 mm or more.
[0026] Next, a method for manufacturing the thermoelectric power generation module in the present embodiment will be described with reference to Figures 2 to 5.
[0027] As shown in Figure 2, cylindrical p-type thermoelectric elements 24a and n-type thermoelectric elements 24b are, for example, 9×9 = 81 pieces / cm 2Prepare a resin thin film 21 embedded at a high density. The p-type thermoelectric element 24a is made of, for example, a BiSbTe chip, and the n-type thermoelectric element 24b is made of a BiTe chip. Electrodes are formed at both ends of the thermoelectric elements 24a and 24b.
[0028] On the other hand, prepare two first and second flexible printed circuit boards 32 and 33 for mounting the thermoelectric elements. The flexible printed circuit boards 32 and 33 are made of a base material made of, for example, polyimide, and their thickness is preferably 5 μm to 40 μm. The wiring layers 35 and 36 formed on the first and second flexible printed circuit boards 32 and 33 are made of, for example, a Cu layer, and their thickness is preferably 8 μm to 35 μm. Further, on the first flexible printed circuit board 32, lead-out electrodes 37a and 37b that are the ends of the wiring layer 35 are formed.
[0029] Next, as shown in FIG. 3, the thermoelectric elements 24a and 24b embedded in the resin thin film 21 are joined to the wiring layer 35 of the first flexible printed circuit board 32 and the wiring layer 36 of the second flexible printed circuit board 33 using, for example, a reflow process of a lead-free solder paste (Sn-Ag-Cu).
[0030] Next, as shown in FIG. 4, the resin thin film 21 is dissolved and removed to complete the thermoelectric power generation module 10. FIG. 5 shows a cross-sectional view of the thermoelectric power generation module 10 along the V-V line of FIG. 4. In FIG. 4, for easy understanding of the structure, the second flexible printed circuit board 33 is shown transparently, and the wiring layer 36 on the lower side, the thermoelectric element chips 24a and 24b, and the wiring layer 35 of the first flexible printed circuit board 32 can be seen.
[0031] The reason for dissolving and removing the resin thin film 21 is to reduce the heat conduction by the resin between the thermoelectric element 24a and 24b chips and increase the temperature difference between both ends of the thermoelectric power generation module.
[0032] Na o、The resin film 21 may be left, but in that case, a resin with a low thermal conductivity is preferable. For example, foamed resins such as foamed polyurethane, foamed polystyrene, and melamine foam are preferable. Also, a silicone resin with a low thermal conductivity is also good.
[0033] Also, as shown in FIG. 6, by providing a slit 51 in the second flexible printed circuit board 33, the thermoelectric power generation module 10 may be made freely bendable.
[0034] Next, in order to obtain a large power generation amount, means for increasing the temperature difference between both ends of the thermoelectric power generation module 10 in a state where the thermoelectric power generation module 10 is attached to a living body will be described.
[0035] The thermal resistance from the living body to the outside air is the sum of the contact thermal resistance between the living body and the thermoelectric power generation module 10, the thermal resistance of the thermoelectric power generation module 10, and the thermal resistance related to heat dissipation from the thermoelectric power generation module 10 to the outside air. In the case of wearable use, since a cooler such as a heat dissipation fin cannot be attached to the outside air side of the thermoelectric power generation module 10, the thermal resistance of heat dissipation from the thermoelectric power generation module 10 to the outside air becomes considerably large, and the temperature difference between both ends of the thermoelectric power generation module cannot be increased as it is.
[0036] Therefore, in the present embodiment, as shown in FIG. 7, a highly heat-dissipative flexible sheet 61 with good heat dissipation is attached to the outside air side of the thermoelectric power generation module 10. As a result, the thermal resistance when heat is dissipated from the thermoelectric power generation module 10 to the outside air can be reduced, and the temperature difference between both ends of the thermoelectric power generation module can be increased.
[0037] In addition, to increase the temperature difference across the thermoelectric power generation module, in addition to reducing the thermal resistance of the outside air from the above-described thermoelectric power generation module 10 using the highly heat-dissipative flexible sheet 61, it is also important to increase the thermal resistance of the thermoelectric power generation module 10. Since the thermal resistance of the thermoelectric power generation module 10 is approximately proportional to the height of the thermoelectric element, it is necessary to increase the height of the thermoelectric element to increase the aspect ratio. For wearable applications, for example, in the case of a cylindrical thermoelectric element, the aspect ratio (= height / diameter of the bottom circle) needs to be at least 1.5 or more.
[0038] According to experiments, when the highly heat-dissipative flexible sheet 61 is attached to the outer surface side of the thermoelectric power generation module 10, if the height of a cylindrical chip with a diameter of 1.0 mm is 2 mm or more, it is possible to make the temperature difference across the thermoelectric power generation module 30% or more of the temperature difference between the living body and the outside air.
[0039] However, the greater the chip height, the greater the thermal resistance and the greater the temperature difference that can be obtained. However, if the chip height is too large, the electrical resistance of the thermoelectric element increases and the output decreases. Therefore, the chip height is preferably 3 mm or less. The practical chip height of the thermoelectric element is preferably 0.8 mm or more and 3 mm or less.
[0040] Next, means for realizing a wearable biosensing device using thermoelectric power generation that has functions such as sensing, managing, and communicating medical data of a living body and can also notify the position information of the living body will be described.
[0041] FIG. 8 is a block diagram showing an example in which a wearable biosensing device using thermoelectric power generation is applied to the case of body temperature measurement.
[0042] As shown in Fig. 8, the power generation output by the thermoelectric power generation module 10 is converted by the DC-DC converter circuit 72 into the power supply voltages necessary to drive a biological sensor 73 such as a body temperature sensor (or a heat flow meter, a heart rate meter), signal processing semiconductor circuits 74 and 75 that amplify and process signals from the biological sensor 73, and a wireless communication semiconductor circuit 76 that transmits the signal-processed data and the individual identification number, respectively. At this time, if necessary, a sensor 77 for measuring the environmental temperature is also mounted.
[0043] The wearable biological sensing device 80 is configured in a form in which components such as the thermoelectric power generation module 10 and semiconductor circuit chips are mounted on a flexible band 81 that can be worn in close contact with a living body, for example, an arm, as shown in Figs. 9(a) and 9(b).
[0044] The wearable biological sensing device 80 illustrated in Figs. 9(a) and 9(b) is composed of a self-powered unit 82 including the thermoelectric power generation module 10 and the DC-DC converter circuit 72, and a biological sensor unit 83 including the biological sensor 73, the signal amplification circuit 74, the signal processing semiconductor circuit 75, and the wireless communication semiconductor circuit 76.
[0045] According to the present embodiment, it is possible to obtain necessary power by constantly adhering to a living body, and to have functions such as sensing, managing, and communicating medical data of the living body, and also to notify the position information of the living body, thereby enabling a wearable biological sensing device. As a result, it is expected that, for example, it will be possible to construct various new preventive medical systems in the future, such as prevention of heat stroke.
[0046] Further, as shown in Fig. 10, the wearable biological sensing device 80 is used as a wearable beacon that periodically and intermittently transmits an individual identification number, and by using it among a large number of receivers 90 installed in a range of several meters to a dozen meters indoors or within a partition, a biological position detection system capable of detecting the position of a living body can be configured using the solid identification numbers received by the large number of receivers 90.
[0047] Also, when a large number of receivers 90 are set, power consumption becomes a problem. However, by securing the power supply for the receivers with the thermoelectric power generation module 10, a battery-less biological position detection system can also be realized.
[0048] Again, while referring to FIG. 4, the configuration of the thermoelectric power generation module 10 in the present embodiment will be described in detail.
[0049] As shown in FIG. 4, the thermoelectric power generation module 10 has thermoelectric elements 24 made of a plurality of cylindrical BiTe-based single crystals, which are sandwiched and mounted between first and second flexible printed boards 32 and 33. Wiring layers 35 and 36 for connecting the thermoelectric elements 24 are formed on the first and second flexible printed boards 32 and 33, respectively. The thermoelectric material of the BiTe-based single crystal is often manufactured in a cylindrical shape, but other shapes may also be used.
[0050] In FIG. 4, for easy understanding of the structure, the second flexible printed board 33 is shown in a transparent manner so that the wiring layer 36 on the lower surface, the thermoelectric element chips 24a and 24b, and the wiring layer 35 of the first flexible printed board 32 can be seen.
[0051] The thermoelectric element 24 consists of a p-type thermoelectric element 24a and an n-type thermoelectric element 24b, and is alternately connected in series in the arrow Y direction by the wiring layers 35 and 36 formed on the first and second flexible printed boards 32 and 33. A plurality of columns of the thermoelectric elements 24 connected in series are arranged in the X direction perpendicular to the Y direction.
[0052] Further, as shown in FIG. 6, a slit 51 may be formed in the Y direction in the second flexible printed circuit board 33 between the columns of the thermoelectric elements 24 connected in series. Thereby, the thermoelectric power generation module 10 can be easily bent in the X direction. When the thermoelectric power generation module 10 is bent along the arm, the outer second flexible printed circuit board 33 has to extend more than the inner first flexible printed circuit board 32 because of the thickness of the thermoelectric power generation module 10, but the slit 51 can secure such extension. The first flexible printed circuit board 32 is formed with lead electrodes 37a and 37b that are the ends of the wiring layer 35.
[0053] Since the thermoelectric power generation module 10 can be easily bent in the X direction around the arm and can be attached closely to the arm, practical power generation can be obtained even with a minute temperature difference between the body temperature and the outside air.
[0054] Instead of forming the slit 51 in the second flexible printed circuit board 33, a base material of an easily stretchable material may be used for the first and second flexible printed circuit boards 32 and 33. Thereby, the thermoelectric power generation module 10 can be bent almost freely. When it is only necessary to be easily stretchable in one direction for attachment to the arm, only one of the first and second flexible printed circuit boards 32 and 33 may use a base material of a stretchable material. As the stretchable base material, for example, a thermosetting elastomer, a silicone resin film, or the like can be used. In addition, polyamide, polycarbonate, a polyolefin film, rubber, and a film in which carbon nanotubes are dispersed for increasing the thermal conductivity in the rubber are also possible. Note that a base material having a high thermal conductivity is desirable. This is because heat loss in the base material can be reduced and the temperature difference in the thermoelectric element 24 can be made as large as possible.
[0055] (Example) As the thermoelectric elements 24a and 24b, columnar BiTe-based single crystal thermoelectric elements having a diameter of 0.7 mm and a height of 2 mm were used respectively. When these thermoelectric elements were arranged with a center axis distance of 1 mm, 1 cm 2In this case, 81 thermoelectric elements can be mounted. The mounting area of the thermoelectric power generation module is configured with two 2.5 cm × 2.5 cm thermoelectric power generation modules so that it can be mounted on a wearable device. At this time, the number of mounted chips of the thermoelectric element was set to 24 × 24 = 576 per thermoelectric power generation module.
[0056] The highly heat-dissipating flexible sheet 61 has a large thermal conductivity of about 40 W / mK, excellent blackbody radiation ability, a large effective surface area due to the unevenness of the sheet surface, and excellent heat dissipation. It was experimentally confirmed that a structure in which a carbon fiber mixed yarn fiber and a carbon sheet with an extremely large in-plane thermal conductivity of 1500 W / mK and a thin thickness are laminated is particularly suitable. As the highly heat-dissipating flexible sheet 61, a structure in which a 25-μm carbon sheet is bonded to a 0.2-mm-thick carbon fiber mixed yarn fiber sheet was used.
[0057] With this thermoelectric power generation module, 60 mV and 75 μW were obtained at a temperature difference of 1°C. As a result, by using two of these thermoelectric power generation modules, 120 mV and 150 μW were obtained, and by combining with a boost converter, a self-powered power supply by thermoelectric power generation capable of driving a wearable biosensing device was realized.
Description of Signs
[0058] 10 Thermoelectric power generation module 21 Resin thin film 24 Thermoelectric element 24a p-type thermoelectric element 24b n-type thermoelectric element 32 First flexible printed circuit board 33 Second flexible printed circuit board 35, 36 Wiring layer 37a, 37b Lead-out electrode 51 Slit 61 Highly heat-dissipating flexible sheet 72 DC converter circuit 73 Biosensor 74 Signal amplification circuit 75 Signal processing semiconductor circuit 76 Wireless communication semiconductor circuit 77 Sensor for measuring environmental temperature 80 Wearable biosensing device 81 Band 82 Self - contained power supply unit 83 Biosensor unit 90 Receiver
Claims
1. A thermoelectric power generation module in which a plurality of p-type thermoelectric elements and n-type thermoelectric elements are alternately connected in series and sandwiched and mounted between first and second flexible printed boards, wherein the p-type thermoelectric elements and the n-type thermoelectric elements are cylinders having a chip size of 1 mm or less and 0.2 mm or more in diameter, a height of 0.8 mm or more and 3 mm or less, and an aspect ratio (height of cylinder / diameter of bottom circle) of 1.5 or more, The mounting density of each of the p-type thermoelectric element and the n-type thermoelectric element is 80 or more per 1 cm 2 and wherein a high heat dissipation flexible sheet is provided outside the outside air side of the thermoelectric power generation module among the first and second flexible printed boards, The high heat dissipation flexible sheet is a thermoelectric power generation module composed of a laminate of carbon fiber mixed yarn and a high thermal conductivity carbon sheet.
2. A thermoelectric power generation module in which a plurality of p-type thermoelectric elements and n-type thermoelectric elements are alternately connected in series and sandwiched and mounted between first and second flexible printed boards, wherein the p-type thermoelectric elements and the n-type thermoelectric elements have a chip size of 1 mm or less and 0.2 mm or more, and a height of 0.8 mm or more and 3 mm or less, wherein a high heat dissipation flexible sheet is provided outside the outside air side of the thermoelectric power generation module among the first and second flexible printed boards, The high heat dissipation flexible sheet is a thermoelectric power generation module composed of a laminate of carbon fiber mixed yarn and a high thermal conductivity carbon sheet.
3. The p-type thermoelectric elements and the n-type thermoelectric elements are embedded in a resin thin film, wherein the first and second flexible printed boards are provided with wiring layers for connecting the p-type thermoelectric elements and the n-type thermoelectric elements formed on both surfaces of the resin thin film, The resin thin film is made of any one of foamed polyurethane, silicone resin, foamed polystyrene, and melamine foam. The thermoelectric power generation module according to claim 2.
4. A wearable beacon that periodically and intermittently transmits an individual identification number, A plurality of stationary receivers that receive the individual identification number transmitted from the wearable beacon, A biological position detection system comprising: The wearable beacon is composed of a wearable biological sensing device, The wearable biological sensing device, The thermoelectric power generation module according to any one of claims 1 to 3, A biological sensor, A processing semiconductor circuit that processes the signal of the sensor, Data processed by the processing semiconductor circuit, A wireless communication semiconductor circuit that transmits an individual identification number, is implemented on a flexible band, the sensor, the semiconductor circuit for processing, and the semiconductor circuit for wireless communication are each driven by the power generation output of the thermoelectric power generation module, A biological position detection system that detects the position of a living body from the individual identification numbers received by the plurality of stationary receivers.
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