Ultrasonic flowmeter and flow rate measurement method

By applying a reference potential to the transducer using a bias circuit before activating the receiving circuit, the ultrasonic flowmeter achieves improved measurement accuracy, addressing the limitations of conventional flowmeters in applications requiring precise fluid flow measurements.

JP7682087B2Active Publication Date: 2025-05-23AZBIL CORP
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Patent Information

Application Number
JP2021203789
Authority / Receiving Office
JP · JP
Patent Type
Patents
Current Assignee / Owner
Filing Date
2021-12-16
Publication Date
2025-05-23
Estimated Expiration
2041-12-16

AI Technical Summary

Technical Problem

Conventional ultrasonic flowmeters face challenges in achieving high measurement accuracy, particularly in applications like gas meters where precise billing measurements are required.

Method used

The ultrasonic flowmeter incorporates a transducer with a bias circuit that applies a reference potential before activating the receiving circuit, ensuring stable transducer potentials and reducing measurement inaccuracies caused by potential fluctuations.

Benefits of technology

This configuration enhances measurement accuracy by stabilizing transducer potentials and minimizing the adverse effects of potential fluctuations, thereby improving the overall performance of the ultrasonic flowmeter.

✦ Generated by Eureka AI based on patent content.

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Patent Text Reader

Abstract

To increase the accuracy of measurement.SOLUTION: The present invention includes: a transducer 11 having a pair of output terminals, the transducer receiving ultrasonic waves; a reception circuit 131 having a pair of input terminals connected to a pair of output terminals with the transducer 11, the reception circuit 131 performing reception processing of the ultrasonic waves received by the transducer 11; and a bias circuit 132-1 for applying a reference potential to the transducer 11. The bias circuit 132-1 applies a reference potential to the transducer 11 before the reception circuit 131 is activated.SELECTED DRAWING: Figure 4
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Description

[Technical field]

[0001] The present disclosure relates to an ultrasonic flowmeter and a flow rate measurement method that measure the flow rate of a fluid using ultrasonic waves. [Background technology]

[0002] Conventionally, ultrasonic flowmeters that use ultrasonic waves to measure the flow rate of a fluid are known (see, for example, Patent Document 1). In these ultrasonic flowmeters, a pair of transducers (ultrasonic piezoelectric elements) are attached to a flow path. In this ultrasonic flowmeter, one of the transducers is driven at a resonant frequency (e.g., 500 kHz) to emit ultrasonic waves. These ultrasonic waves propagate and excite the other transducer, which is then amplified to obtain a received signal. In this ultrasonic flowmeter, the propagation time can be measured by measuring the time between the transmission of the ultrasonic waves and the arrival of the received signal. The ultrasonic flowmeter performs the same operation by switching between transmission and reception on the upstream and downstream sides, and obtains the propagation time difference by comparing the two. In principle, when there is no flow rate, the propagation time difference is zero. On the other hand, when there is a flow rate, a propagation time difference occurs according to the flow rate. In this way, the ultrasonic flowmeter measures the flow rate. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2020-134439 A Summary of the Invention [Problem to be solved by the invention]

[0004] For example, high measurement accuracy is required for gas meters and other devices related to billing for gas usage, and ultrasonic flow meters are therefore always required to have higher accuracy.

[0005] The present disclosure is devised to solve the above-mentioned problems, and has an object to provide an ultrasonic flowmeter and a flow rate measurement method that can improve measurement accuracy compared to conventional techniques. [Means for solving the problem]

[0006] The ultrasonic flowmeter according to the present disclosure comprises a transducer having a pair of output terminals and receiving ultrasonic waves, a receiving circuit having a pair of input terminals connected to the pair of output terminals of the transducer and performing reception processing on the ultrasonic waves received by the transducer, and a bias circuit applying a reference potential to the transducer, wherein the bias circuit applies the reference potential to the transducer before starting up the receiving circuit. Effect of the Invention

[0007] According to the present disclosure, since it is configured as described above, it is possible to improve the measurement accuracy compared to the conventional art. [Brief description of the drawings]

[0008] [Figure 1] 1 is a diagram illustrating a configuration example of an ultrasonic flowmeter according to a first embodiment. [Diagram 2] FIG. 2 is a diagram illustrating a configuration example of a transmitting / receiving section in the first embodiment. [Diagram 3] 3A and 3B are diagrams illustrating an example of mounting a transducer in the first embodiment. [Figure 4] FIG. 2 is a diagram illustrating an example of the configuration of a receiving unit according to the first embodiment. [Diagram 5] FIG. 11 is a diagram illustrating an example of the configuration of a receiving unit in the second embodiment. [Figure 6] FIG. 11 is a diagram illustrating an example of the configuration of a receiving circuit control unit in the second embodiment. [Figure 7] 11 is a flowchart showing an example of a process performed by a transmitting / receiving unit in the second embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. Embodiment 1 FIG. 1 is a diagram showing a configuration example of an ultrasonic flowmeter according to a first embodiment. An ultrasonic flowmeter uses ultrasonic waves to measure the flow rate of a fluid to be measured. This ultrasonic flowmeter is applied to, for example, a gas meter and measures the flow rate of gas. As shown in FIG. 1, this ultrasonic flowmeter includes a transmitting / receiving unit (first transmitting / receiving unit) 1-1, a transmitting / receiving unit (second transmitting / receiving unit) 1-2, and a measuring unit 2.

[0010] In this case, when the same component exists in multiple systems, the suffix (-1, -2, ...) for each system is added to the reference numeral indicating the component, and when there is no particular need to distinguish, the suffix is ​​not added. In addition, for configurations that have the same function but different suffixes, only the one with the suffix "-1" is illustrated, and the configurations with other suffixes are not illustrated.

[0011] The transmitting / receiving unit 1-1 transmits and receives ultrasonic waves to and from the transmitting / receiving unit 1-2. As shown in Fig. 2, the transmitting / receiving unit 1-1 includes a transducer (first transducer) 11-1, a transmitting unit (first transmitting unit) 12-1, and a receiving unit (first receiving unit) 13-1.

[0012] 3, the transducer 11-1 is attached to one side (e.g., the upstream side) of a flow path 5 through which a fluid to be measured flows. The transducer 11-1 is driven by a transmitting unit 12-1 to transmit ultrasonic waves toward the other side (e.g., the downstream side) of the flow path 5. The transducer 11-1 also receives ultrasonic waves transmitted from the other side of the flow path 5. The transducer 11-1 has a pair of output terminals.

[0013] The transmitter 12-1 drives the transducer 11-1. The receiving section 13-1 performs reception processing on the ultrasonic waves received by the transducer 11-1.

[0014] The transmitting / receiving unit 1-2 transmits and receives ultrasonic waves to and from the transmitting / receiving unit 1-1. The transmitting / receiving unit 1-2 includes a transducer (second transducer) 11-2, a transmitting unit (second transmitting unit) 12-2, and a receiving unit (second receiving unit) 13-2, similar to the transmitting / receiving unit 1-1 shown in FIG.

[0015] 3, the transducer 11-2 is attached to the other side of the flow path 5. The transducer 11-2 is driven by a transmitting unit 12-2 and transmits ultrasonic waves toward one side of the flow path 5. The transducer 11-2 also receives ultrasonic waves transmitted from one side of the flow path 5. The transducer 11-2 has a pair of output terminals.

[0016] The transmitter 12-2 drives the transducer 11-2. The receiving section 13-2 performs reception processing on the ultrasonic waves received by the transducer 11-2.

[0017] The measurement unit 2 measures the flow rate of the fluid based on the transmission and reception results by the transmission and reception units 1-1 and 1-2. At this time, the measurement unit 2 calculates the difference between the time taken for the ultrasonic waves transmitted by the transmission and reception unit 1-1 to be received by the transmission and reception unit 1-2 and the time taken for the ultrasonic waves transmitted by the transmission and reception unit 1-2 to be received by the transmission and reception unit 1-1, and calculates (measures) the flow rate of the fluid flowing through the flow path 5 from the time difference.

[0018] Next, a configuration example of the receiving unit 13-1 will be described with reference to FIG. As shown in FIG. 4, the receiving unit 13-1 includes a receiving circuit (first receiving circuit) 131-1 and a bias circuit (first bias circuit) 132-1.

[0019] The receiving circuit 131-1 has a pair of input terminals. One of the pair of input terminals of the receiving circuit 131-1 is connected to one of the pair of output terminals of the transducer 11-1, and the other of the pair of input terminals is connected to the other of the pair of output terminals of the transducer 11-1. This receiving circuit 131-1 performs a receiving process on the ultrasonic wave (signal) received by the transducer 11-1. That is, the receiving circuit 131-1 amplifies the ultrasonic wave (signal) received by the transducer 11-1 and cuts the band of the ultrasonic wave (signal) by a bandpass filter.

[0020] The bias circuit 132-1 applies a reference potential (bias voltage) to the transducer 11-1 when the bias circuit 132-1 is activated (activated state). In other words, when the bias circuit 132-1 is activated, it raises the potential of the transducer 11-1 to a reference potential (bias voltage) for the receiving circuit 131-1 to receive ultrasonic waves. The reference potential is the central potential of the ultrasonic waves to be received. As a result, the reference potential is set to a voltage sufficient for the amplitude of the ultrasonic waves to be received.

[0021] The receiving circuit 131-1 and the bias circuit 132-1 are controlled independently of each other in terms of power supply. Therefore, the bias circuit 132-1 can maintain the activated state regardless of whether the receiving circuit 131-1 is activated (activated state) or deactivated (deactivated state). For example, in a state where power is supplied to the transmitting / receiving unit 1-1, the bias circuit 132-1 maintains the activated state, and the receiving circuit 131-1 performs intermittent driving in which the activated state and the deactivated state are alternately switched. Specifically, in a state where power is supplied to the transmitting / receiving unit 1-1, the bias circuit 132-1 maintains the activated state and applies a reference potential to the transducer 11-1 before the receiving circuit 131-1 is activated, and the receiving circuit 131-1 performs intermittent driving in which the activated state and the deactivated state are alternately switched while the reference potential is applied to the transducer 11-1 by the bias circuit 132-1. The bias circuit 132-1 may be driven intermittently so as to enter the stopped state at the same time as the receiving circuit 131-1 and then enter the activated state before the receiving circuit 131-1.

[0022] Similarly to the receiving unit 13-1 shown in FIG. 4, the receiving unit 13-2 includes a receiving circuit (second receiving circuit) 131-2 and a bias circuit (second bias circuit) 132-2.

[0023] The receiving circuit 131-2 has a pair of input terminals. One of the pair of input terminals of the receiving circuit 131-2 is connected to one of the pair of output terminals of the transducer 11-2, and the other of the pair of input terminals is connected to the other of the pair of output terminals of the transducer 11-2. The receiving circuit 131-2 performs a receiving process on the ultrasonic wave (signal) received by the transducer 11-2. That is, the receiving circuit 131-2 amplifies the ultrasonic wave (signal) received by the transducer 11-2 and cuts the band of the ultrasonic wave (signal) by a bandpass filter.

[0024] 4, the bias circuit 132-2 applies a reference potential (bias voltage) to the transducer 11-2 in the activated state. In other words, the bias circuit 132-2 in the activated state increases the potential of the transducer 11-2 to a reference potential (bias voltage) for the receiving circuit 131-2 to receive ultrasonic waves.

[0025] The receiving circuit 131-2 and the bias circuit 132-2 have independent power supply paths. Therefore, the bias circuit 132-2 can maintain an active state regardless of whether the receiving circuit 131-2 is active (active state) or not (not active state). For example, in a state where power is supplied to the transmitting / receiving unit 1-2, the bias circuit 132-2 maintains an active state, and the receiving circuit 131-2 performs intermittent driving in which the active state and the not active state are alternately switched. Specifically, in a state where power is supplied to the transmitting / receiving unit 1-2, the bias circuit 132-2 maintains an active state and applies a reference potential to the transducer 11-2 before starting the receiving circuit 131-2, and the receiving circuit 131-2 performs intermittent driving in which the active state and the not active state are alternately switched while the reference potential is applied to the transducer 11-2 by the bias circuit 132-2.

[0026] Next, the effects of the ultrasonic flowmeter according to the first embodiment will be described. Here, the ultrasonic flowmeters (ultrasonic gas flowmeters) used as gas meters are often battery-powered. Therefore, in order to reduce power consumption, such ultrasonic flowmeters generally have a configuration in which the receiving circuit (internal circuit) is intermittently driven and the power is turned off except when receiving signals, i.e., the power supply is stopped.

[0027] On the other hand, depending on the configuration of the transducer and the receiving circuit selected according to the application or size of the ultrasonic flowmeter, a problem may occur in which the fluctuation in potential (electrical fluctuation) caused by the start-up (rising) of the receiving circuit adversely affects the measurement accuracy. Specifically, in an ultrasonic flowmeter in which a bias circuit is built into the receiving circuit, or in which the receiving circuit and the bias circuit share a power supply path, the bias circuit is started when the receiving circuit is started every time a signal is received, and the fluctuation in potential caused by the start-up is transmitted to the transducer. Since the fluctuation in potential is not completely symmetrical between the P side and the N side shown in FIG. 4, a potential difference occurs at both ends of the transducer, and the fluctuation in potential is converted into a physical vibration of the transducer and is held. Then, the held vibration is superimposed on the receiving signal that arrives later, adversely affecting the measurement accuracy.

[0028] In order to prevent this, in the ultrasonic flowmeter according to the first embodiment, as shown in Fig. 4, the receiving circuit 131 and the bias circuit 132 are formed independently in the receiving unit 13, and the bias circuit 132 is configured to be able to maintain the activated state regardless of the activated state or the terminated state of the receiving circuit 131. As a result, in the ultrasonic flowmeter according to the first embodiment, the reference potential can be applied to the transducer 11 already when the receiving circuit 131 performs a receiving operation, so that the potentials at both ends of the transducer 11 can be made the same or the potential difference can be sufficiently reduced, and the vibration of the transducer 11 can be suppressed. Note that by measuring the flow rate after a sufficient time has elapsed since power is supplied to the transmitting / receiving unit 1, that is, from when the bias circuit 132 is activated until the vibration of the transducer 11 subsides, it is possible to perform a more accurate flow rate measurement.

[0029] As described above, according to the first embodiment, the ultrasonic flowmeter includes a transducer 11 having a pair of output terminals and receiving ultrasonic waves, a receiving circuit 131 having a pair of input terminals connected to the pair of output terminals of the transducer 11 and performing reception processing on the ultrasonic waves received by the transducer 11, and a bias circuit 132 applying a reference potential to the transducer 11, and the bias circuit 132 is configured to apply the reference potential to the transducer 11 before starting up the receiving circuit 131. This makes it possible for the ultrasonic flowmeter according to the first embodiment to have improved measurement accuracy compared to conventional ones.

[0030] Embodiment 2 Hereinafter, the second embodiment will be described with reference to Fig. 2 and Fig. 5 to Fig. 7. The ultrasonic flowmeter according to the second embodiment has a different configuration of a receiving unit from the ultrasonic flowmeter according to the first embodiment, but other configurations are the same as those of the ultrasonic flowmeter according to the first embodiment, so that a duplicated description will be omitted.

[0031] 2, the transmitting / receiving unit (first transmitting / receiving unit) 1A-1 of the ultrasonic flowmeter according to the second embodiment includes a transducer 11-1, a transmitting unit 12-1, and a receiving unit 13A-1. The ultrasonic flowmeter according to the second embodiment includes the transmitting / receiving unit (first transmitting / receiving unit) 1A-1 and the transmitting / receiving unit (second transmitting / receiving unit) like the ultrasonic flowmeter according to the first embodiment, but the configurations of the transmitting / receiving unit (first transmitting / receiving unit) 1A-1 and the transmitting / receiving unit (second transmitting / receiving unit) are the same, so that hereinafter, the transmitting / receiving unit (first transmitting / receiving unit) 1A-1 will be described, and the description of the transmitting / receiving unit (second transmitting / receiving unit) will be omitted.

[0032] 5, the receiving unit 13A-1 includes a receiving circuit 131-1, a bias circuit 132-1, and a receiving circuit control unit 133-1. The receiving circuit control unit 133-1 is connected to the receiving circuit 131-1 and controls switching between an active state and an inactive state of the receiving circuit 131-1. For example, when power is supplied to the transmitting / receiving unit 1A-1, the bias circuit 132-1 maintains the active state.

[0033] For example, as shown in FIG. 6, the receiving circuit control section 133-1 has a timer section 1331-1 and a switching section 1332-1.

[0034] For example, the timer 1331-1 starts timing when power is supplied to the transmitter / receiver 1-1. When the time counted by the timer 1331-1 reaches a predetermined time, the switch 1332-1 sets the receiving circuit 131-1 to a startable state, that is, a state in which the receiving circuit 131-1 can be switched from a stopped state to a started state. The predetermined time is a time from when the transmitting / receiving unit 1-1 is supplied with power, that is, when the bias circuit 132-1 is in a started state, until the fluctuation in the potential of the transducer 11-1 caused by the start falls within an allowable range (for example, a time from when the bias circuit 132-1 is started to when the transducer 11-1 is in a statically settled state). That is, when the predetermined time has elapsed from the start of the bias circuit 132-1, the switch 1332-1 determines that the fluctuation in the potential of the transducer 11-1 caused by the start of the bias circuit 132-1 falls within an allowable range, and sets the receiving circuit 131-1 to a startable state in a state in which the fluctuation in the potential has settled. The predetermined time is set in advance as a set value by simulation or actual measurement.

[0035] The reception circuit control unit 133-1 is realized by a processing circuit such as a system LSI (Large Scale Integration), or a CPU (Central Processing Unit) that executes a program stored in a memory or the like.

[0036] Next, a flow rate measuring method using the ultrasonic flowmeter of the second embodiment will be described. FIG. 7 is a flowchart showing an example of a process performed when the ultrasonic flowmeter performs flow rate measurement. The ultrasonic flowmeter first drives a transducer in the transmission section of one of the transmission / reception sections, and transmits ultrasonic waves by the transducer (step ST1). After performing the process of step ST1, the ultrasonic flowmeter starts the bias circuit 132 of the transmission / reception section 1A-1, which is the other transmission / reception section (step ST2). In this process, the transmission / reception section 1A-1 applies a reference potential to the transducer 11-1 by the bias circuit 132. Also, in this process, the transmission / reception section 1A-1 starts timing, for example, by the timer section 1331-1.

[0037] Next, the ultrasonic flowmeter starts the receiving circuit 131-1 of the transmitting / receiving unit 1A-1 (step ST3). In other words, the transmitting / receiving unit 1A-1 starts the receiving circuit 131-1 after starting the bias circuit 132. Also, in other words, the transmitting / receiving unit 1A-1 starts the receiving circuit 131-1 after the bias circuit 132 applies a reference potential to the transducer 11. In this process, the transmitting / receiving unit 1A-1 starts the receiving circuit 131-1 based on the receiving circuit 131-1 being in a startable state by the receiving circuit control unit 133-1. For example, the transmitting / receiving unit 1A-1 starts the receiving circuit 131-1 based on the switching unit 1332-1 putting the receiving circuit 131-1 in a startable state based on the time counted by the timer unit 1331-1 reaching a predetermined time.

[0038] After the process of step ST3 is performed, when the receiving circuit 131-1, which is the other transmitting / receiving unit, receives ultrasonic waves transmitted from one transmitting / receiving unit while the receiving circuit 131-1 is activated (YES in step ST4), the transmitting / receiving unit 1A-1 causes the receiving circuit 131-1 to perform reception processing (step ST5). Note that the receiving unit 1A-1 may be configured to maintain a state in which it is capable of receiving ultrasonic waves while a current is being supplied to the device, or may be configured to end the state in which it is capable of receiving ultrasonic waves (time out) if a predetermined time has passed since it became capable of receiving ultrasonic waves without receiving ultrasonic waves.

[0039] When the transmitting / receiving unit 1A-1 drives the receiving circuit 131-1 intermittently, the transmitting / receiving unit 1A-1 repeats the processes from step ST2 to step ST6. For example, the transmitting / receiving unit 1A-1 drives the receiving circuit 131-1 intermittently to cause the measuring unit 2 to calculate a difference between the time taken for an ultrasonic wave transmitted by one transmitting / receiving unit to be received by the other transmitting / receiving unit and the time taken for an ultrasonic wave transmitted by the other transmitting / receiving unit to be received by the one transmitting / receiving unit multiple times and calculate an average value of the time differences, thereby improving the accuracy of the flow rate measurement of the fluid flowing through the flow path 5.

[0040] In the ultrasonic flowmeter according to the second embodiment, when power is supplied to the transmitting / receiving unit 1A, the bias circuit 132 is started, the receiving circuit control unit 133 measures the time since the bias circuit 132 was started, and the receiving circuit 131 is put into a state in which it can be started after a predetermined time has elapsed since the bias circuit 132 was started, but this is not limiting. The ultrasonic flowmeter only needs to be configured so that the bias circuit applies a reference potential to the transducer at least before the receiving circuit is started and put into a state in which it can perform measurement.

[0041] For example, the ultrasonic flowmeter may be configured such that the receiver circuit control unit controls the activation of the bias circuit and the receiver circuit. For example, in the ultrasonic flowmeter, the receiver circuit control unit may activate the bias circuit in response to a predetermined trigger while power is being supplied to the transmitter / receiver unit, and may activate the receiver circuit after a predetermined time has elapsed since the bias circuit was activated, or may set the receiver circuit in an activatable state after the predetermined time has elapsed.

[0042] Also, for example, the ultrasonic flowmeter may have a signal transmission unit in which the bias circuit transmits a signal to the receiving circuit control unit, and the receiving circuit may be started based on the receiving circuit control unit receiving a signal from the bias circuit, or the receiving circuit may be put into a startable state based on the receiving circuit control unit receiving a signal from the bias circuit. Specifically, the ultrasonic flowmeter may have a clock unit in which the bias circuit measures time, and the signal transmission unit transmits a signal to the receiving circuit control unit based on the time measured by the clock unit since the bias circuit was started reaching a predetermined time, and the receiving circuit may be started based on the receiving circuit control unit receiving a signal from the bias circuit, or the receiving circuit may be put into a startable state based on the receiving circuit control unit receiving a signal from the bias circuit.

[0043] Also, for example, an ultrasonic flowmeter may have a signal transmitting unit in which the bias circuit transmits a signal to a receiving circuit control unit, and a potential detection unit that detects (measures) fluctuations in the transducer's potential, and based on the fact that the fluctuations in the transducer's potential detected by the detection unit are within an acceptable range, the signal transmitting unit may transmit a signal to the receiving circuit control unit, and based on the receiving circuit control unit receiving a signal from the bias circuit, the receiving circuit may be started, or based on the receiving circuit control unit receiving a signal from the bias circuit, the receiving circuit may be put into a state in which it can be started.

[0044] In the above-described embodiment, the ultrasonic flowmeter has two transducers provided for each of the two transmitting / receiving units, but is not limited thereto. For example, the ultrasonic flowmeter may be configured such that two transducers arranged on one side and the other side of the flow path share one transmitting / receiving unit.

[0045] Furthermore, within the scope of the present disclosure, any of the components of the embodiments may be modified, combined, or any of the components of the embodiments may be omitted. [Explanation of symbols]

[0046] 1, 1A Transmitter / Receiver 2. Measurement section 5 Flow Path 11 Transducer 12 Transmitter 13, 13A Receiver 131 Receiver circuit 132 Bias Circuit 133 Receiving circuit control section 1331 Timing section 1332 Switching section

Claims

1. a transducer having a pair of output terminals for receiving ultrasonic waves; a receiving circuit having a pair of input terminals connected to a pair of output terminals of the transducer, and performing receiving processing on the ultrasonic waves received by the transducer; a bias circuit for applying a reference potential to the transducer; The bias circuit applies a reference potential to the transducer before the receiving circuit is activated.

1. An ultrasonic flow meter comprising:

2. a receiving circuit control unit that starts the receiving circuit while the bias circuit applies a reference potential to the transducer; 2. The ultrasonic flowmeter according to claim 1.

3. The receiving circuit control unit starts the receiving circuit in a state where a fluctuation in potential caused by the start-up of the bias circuit falls within a tolerable range.

3. The ultrasonic flowmeter according to claim 2.

4. A flow rate measurement method performed by an ultrasonic flow meter including a transducer having a pair of output terminals, a receiving circuit having a pair of input terminals connected to the pair of output terminals of the transducer, and a bias circuit, comprising: the bias circuit applying a reference potential to the transducer; the receiving circuit starting up after the bias circuit applies a reference potential to the transducer; receiving ultrasonic waves with the transducer and the receiving circuitry active; The receiving circuit performs a receiving process on the ultrasonic waves received by the transducer. A flow rate measuring method comprising:

Citation Information

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