Bluetooth Low-Energy Current Sensor Compensated Using Piecewise Linear Model

2.1 Principle of a Current Sensor using Hall Effect

An open-loop current sensor measures the current flowing through a conductor, thus sensing the magnetic force generated in the gaps of the magnetic core. For the sensed voltage, an amplified compensation circuit is used. The generated Hall voltage can be expressed as:

where K is a proportionality coefficient, Ic is the current applied to the Hall sensor, and B is the external magnetic flux density. When a current flows, a magnetic flux is generated in the core of the magnetic body, and a magnetic force proportional to the magnitude of the magnetic flux generates a Hall voltage in the gaps of the core. A voltage of several millivolts is generated in the Hall element, which confirms the magnitude of the magnetic force. An operational amplifier can be used to amplify the output of the Hall element and measure this output as a value proportional to the current to be measured [12, 13].

2.1.1 Composition of Hall Current Sensor: Hall Element and Hall IC

Typically, a current sensor using a Hall element consists of a Hall IC, Hall element, magnetic body, and amplifying circuit. As shown in Table 2, this type of current sensor exhibits different properties depending on the characteristics of each material [12, 15]. A Hall element is a magnetic sensor that responds to magnetic fields and generally exhibits an output voltage proportional to the magnetic field. Common examples of Hall element materials include indium antimonide, indium arsenide, germanium, silicon, and gallium arsenide. A Hall IC is a combination of a compound semiconductor and a Hall element with a silicon signal-processing circuit chip [12, 14].

Table 2.

Materials and characteristics of Hall element.

A Hall IC is a combination of a compound semiconductor and a Hall element with a silicon signal-processing circuit chip [12, 14]. A Hall element is an indirect-gap semiconductor as well as a wave vector semiconductor that has different electric and electronic fields. As shown in Table 2, recombination using gallium arsenide is a direct method that has greater electron mobility than that of silicon. However, gallium arsenide has the disadvantages of low heat conductivity, low intensity integration, and higher processing cost than that of normal silicon. A Hall element is made of a Gallium arsenide material but is not a high-speed analog integrated circuit [12, 14].

In this study, a Hall element with an HG-302A (AKM) sensor, which is 2.35 mm wide, 2.7 mm long, and 0.95 mm thick, was produced. The operating temperature range of the Hall sensors varies from -40 ^oC to 125 ^oC.

2.1.2 Magnetic Material

A magnetic field around a steel core occurs when a current flows through a wire crossing a magnetic core with an air gap.

Table 3 lists the magnetic materials used in current sensors [15]. Magnetic materials used in such sensors must exhibit a high permeability, high magnetic flux density, and superior saturation properties, as well as a low coercivity and low temperature dependence. However, a material with high permeability exhibits poor saturation and temperature characteristics. By contrast, materials with low permeability exhibit good saturation and temperature characteristics but poor heat-generation characteristics at high frequencies because of coercivity and iron loss. Therefore, a suitable magnetic material must be selected, based on the current measurement environment (Table 3). Silicon steel was selected as the core material for the proposed current sensor, owing to its high magnetic permeability, magnetic flux density, and saturation characteristics, as well as its low coercivity and temperature-change characteristics. Steel frames based on magnetic materials are divided into a winding coil and laminated layer according to the stratification method used. The core of the current sensor produced in this study is a directional steel core. Because the steel core is an air-gap type, the magnetic permeability is high when the magnetic field is generated in a form consistent with the direction of the steel core.

Table 3.

Characteristics of magnetic materials.

2.1.3 Amplifying Circuit

A current sensor measures the current and indicates the output of the voltage or current. To measure a magnetic field, the circuit is considered to consist of a magnetic core, a Hall element, and other electronic circuits. To express the flow of motion, an electrostatic current is supplied to operate the Hall element to measure the stimulation of the magnetic core material; subsequently, the aperture signal is output as shown in Fig. 1. In addition, the zero-offset temperature compensation of the Hall element compensates for the error characteristics according to the temperature. The phase compensation is applied by employing the compensation conditions according to the type of operational amplifier (op-amp) used, as shown in Fig. 1. In this study, an OPA2374 (Texas Instruments) op-amp was used. The expression is defined as [16]:

Fig. 1.

Principles of open-loop current sensors with Hall element.

$\[ {\mathit{V}}_{\mathit{o}\mathit{u}\mathit{t}}=\frac{R2}{R1}\left(\mathit{V}2-\mathit{V}1\right) \]$

(2)

3.1 Hardware Configuration of Bluetooth Current Sensor Node

Fig. 3(a) shows a schematic of the BLE current sensor. The BLE includes terminals that control the current sensor nodes and access the network.

Fig. 3.

(a) Configuration diagram, (b) flow chart of the BLE current sensor using module initialization method.

Fig. 3(b) shows a flowchart of the initialization module. The hardware configuration is based on the BLE wireless protocol and Android application communication function. To display the measured analog current digitally, an ADC is used to measure the read value at the sensor node and the sensed value at a user’s request, thereby initiating an ADC cycle change. An nRF52832 chip (Nordic semiconductor) that supports BLE wireless communication is used along with a 32-bit ARM Cortex M4F processor, 512 kB of flash memory, and 64 kB of SRAM. For the clock source, a 32-kHz clock can be generated internally, or a crystal can be attached externally. An external low-power 32-kHz crystal is used to increase precision. For the power supply, a DC/DC converter with low-power characteristics is used with an LC circuit in an nRF52 chip, to convert the voltage within the range of 1.7 to 3.3 V to the operating voltage of 1.3 V required by the IC [19]. A simple circuit is used for converting the analog signal (current) into a digital signal. This study also uses a successive approximation (SA) method that satisfies the requirements of both the cost and speed. Differential nonlinearity (DNL) and integral nonlinearity (INL), which are indicators of ADC nonlinearity based on a 10-bit resolution, exhibit good performance. When measuring the voltage through a SA-ADC, the converter first operates in differential mode with a 12-bit resolution to increase the signal-to-noise ratio (SNR). Subsequently, it operates in oversampling mode; the analog voltage is measured 16 times, after which the values are averaged and converted into a digital voltage. In addition, to use the temperature sensor for controlling the I²C serial communication, a two-wired interface (TWI) module, which provides a serial communication similar to that supported by the nRF52832 chip, is used. A watchdog timer is set to intervals of 30 s to reset the board in the event of temporary failures [20, 21].

3.2 Software Flowchart of Bluetooth Current Sensor

The application for the proposed BLE current sensor initializes the ADC, communication unit, and timer unit of the Bluetooth sensor node (see Fig. 4).

Fig. 4.

Flowchart of proposed application program behavior.

The output voltage and ambient temperature are measured at regular intervals preset by the user. When the terminal is connected to the Bluetooth sensor node, the compensation table is received from the terminal, according to the temperature interval. The information to correct the voltage, rather than increase or average the measured data of the temperature interval, is obtained. Based on the current sensor output value, which depends on the temperature interval, the correction information is classified, as shown in Fig. 4, and is appropriately applied when the temperature interval changes. When the temperature interval and correction voltage information are given, the measured voltage value approximated by the piecewise linear model is corrected. If the Bluetooth sensor node and terminal are not connected, the process returns to the initialization step and repeats the measurement. When connected to the terminal, measurement is conducted by the current sensor according to the temperature measured by the temperature sensor, and the converted output voltage is approximated and compensated using the piecewise linear model. Compensating for software offset enables the system to provide a current value with a small error, and a miniaturized Bluetooth current sensor can be used without separate devices.

3.3 Empirical Compensation Equation

An empirical equation that compensates for the analog signal from the current sensor through a piecewise linear model that breaks down the voltage ranges for the measured current value can be expressed as follows:

where Vm is the measured current sensor voltage, and k-values representing the information in the interval are integers between zero and 8. If the input voltage value representing the section of the measured voltage to be corrected for a specific temperature interval is assumed to be A0–A9 (ideal case), the output voltage value of the current sensor is assumed to be B0–B9, and the measurement for a voltage value of lower than A0 is between A_k and A_k+1, the measurement voltage is approximated according to Eq. (3). Thus, a voltage of greater than A9 can be calculated by compensating for the voltage. The compensation information in Table 5 shows that the horizontal axis corresponds to the output voltage of the current sensor, which varies with temperature, and that the longitudinal axis corresponds to the output voltage of the ideal current sensor. When information regarding the calibration of the output voltage of the current sensor is obtained, it can be corrected in the following ways.

3.4 Reliability Verification of Proposed Bluetooth Sensor Offset

In the case of the proposed BLE current sensor, the software compensates the offset based on the compensation table given by the mobile terminal or the server to provide a smaller current with a smaller error. Thus, the offset is compensated without including any additional device to provide a smaller BLE current sensor. For the piecewise linear model, the ideal output of the current sensor is given to approximate its nonlinearity. However, as the ambient temperature is not fixed in an actual environment, correction tables (Tables 4 and 5) for calculating the output voltage interval according to the temperature can be displayed. In the corresponding graph derived from the values in the table, the horizontal axis represents the output voltage of the current sensor, which changes with temperature, and the vertical axis represents the output voltage of the ideal current sensor. Table 4 shows the output voltage value of the current sensor measured at a given temperature, and Table 5 lists the values for compensating the output voltage value of the current sensor according to the temperature interval. The compensation of the current values measured by the current sensors can be applied using a partially linear model by dividing the voltage intervals for a given measured current. To approximate the nonlinear characteristics of the current sensor with a partially linear model, information regarding the ideal output value of the current sensor and the actual output value is required according to the temperature. As shown in Table 4, the average value of the specific current sensor output voltage is calculated at −10 ^oC, − 5 ^oC, 0 ^oC, and 10 ^oC. Table 5 shows the compensation information for sections 50 ^oC – 85 ^oC and at 0 ^oC to 30 ^oC. Voltage correction information can be obtained in a direction that reduces errors. Once the calibration information of the current sensor output voltage for the temperature interval is obtained, a compensation experiment (3) can be conducted to calibrate the specific voltage value approximated using the partial linear model (see Fig. 5).

Table 4.

Measurement value of current sensor according to temperature section.

Table 5.

Corrected output value according to temperature interval

Fig. 5.

Compensation graph.

3.5 Fabrication of Proposed Smart Current Sensor

The proposed smart current sensor was designed to digitize the analog output of the current sensor and transmit data to the application via Bluetooth communication. Fig. 6 shows the proposed smart current sensor circuit. The proposed BLE current sensor can be divided into the current sensor unit and the Bluetooth unit.

Fig. 6.

(a) Proposed BLE current sensor, (b) laminated BLE current sensor module.

Fig. 6(a) shows the proposed smart current sensor. The dimensions of the silicon steel core are as follows: inner diameter of 8 mm, an outer diameter of 12 mm, a thickness of 10 mm, and an air gap of 1.5 mm. As shown in Fig. 1, the Hall element is inserted between the pores of the silicon steel, and when the magnetic field is applied to the Hall element, the Hall voltage is amplified relative to the magnitude of the magnetic field, as shown in Eq. (2). Fig. 6(b) shows the DC/DC converter used to control the difference between voltages [11]. The characteristic frequency of the current sensor is 25 kHz. The linearity of the output relative to the rated current is 1%. The circuit of the BLE current sensor is stacked to achieve a ground design that does not cause errors owing to interference between the current sensor, controller, and Bluetooth device. This also minimizes the footprint of the circuit.

Fig. 7 shows the configuration of the Android app used in the completed Bluetooth current sensor experiment. When the monitoring app is launched on a phone screen, it scans the area for 10 s to detect nearby BLE devices. After finding the available BLE devices, the user selects the device to be connected. A connection with the BLE device is established and information is then exchanged between the app and BLE device. The connection status, temperature received from the smart sensor node, data communication cycle, current sensor model number, and measured current can be monitored through the smartphone app. The measured current value can be saved as a text file (Fig. 7(b)). The data are stored from the time the user presses the “Start” button until when the user presses “Stop” on the application screen.

Fig. 7.

Proposed BLE current sensor application: (a) configuration, (b) data channels.

4.1 Measurements and Tests

Experiments were conducted based on the theoretical backgrounds of the current sensor and the currently used methods. A voltage of ±15 V was supplied to drive the current sensor; in addition, DC (KIKUSUI PWR1600L) and AC (KAST S2307180) devices were used to provide the wire current flows for the measurements, and a stable current was therefore supplied. To inspect the linearity of the Bluetooth current sensor for a 4 V output at a rating of 50 A, we increased the current in steps of 5 A; compared the information displayed in the BLE sensor, PCB output stage, and screen of the cell-phone application; and, evaluated the measurement accuracy. Here, two multimode (KEYSIGHT 34461A) measuring devices were connected to measure the output signals of the BLE sensor and PCB separately. The direct and alternating currents were measured using different power sources, and the linearity and accuracy of the output values were plotted as shown in Fig. 8 [12]. In addition, an experiment was conducted to compensate for the temperature of the current sensor for other input currents, and the results were tested using an anti-temperature humidifier (JEIOTECH HG-G-1000) for 10 s, by varying the input current and reaching a temperature of −10 °C to 85 °C.

Fig. 8.

Schematic of proposed BLE current sensor experiment.

4.2 Experimental Results of the Proposed Bluetooth Sensor

After installing the proposed sensor in various environments, to evaluate the accuracy of the measured output displayed on the smartphone, we compared the outputs of the proposed sensor and the power supply. We evaluated the accuracies of the same measurements in both the sensor PCB and application. We also compared the output value for the input current with direct and alternating currents (see Fig. 9(a) and (b)). Simultaneously, to measure the ideal output values for the input current and output voltage of the sensor, PCB, and application, and to evaluate the accuracy of the measurements for each input voltage, we increased the input voltage in 5 A increments from 0 to 50 A, and compared the voltage measured at each part by the sensor, PCB, and application. To measure and monitor the output voltage values in the DC and AC areas, the output for each input value was measured at three positions using the smartphone app screen and two digital multimeters. Fig. 9 shows the linearity and accuracy of the measured values of the current sensor.

Fig. 9.

Comparison of measurement data from different parts with input current: (a) Comparison of direct current measurements, (b) comparison of alternating current measurements, (c) a comparison graph.

The entire area showed linearity within 1%, and the current sensor, PCB, and app exhibited stable values within 0.05% for the input current when comparing the error rates for the DC and AC measurements. At 45 A, the value measured by the sensor showed the highest rate of change, with an output voltage of 0.1 V. Compared to the rest of the area, this value was also stable within 1%. To evaluate the Bluetooth sensor for comparison, this study measured the current flowing through the wire under the same load conditions. The current input into the Bluetooth sensor, the current flowing through the PCB, and the value measured by the Bluetooth sensor and displayed on the tablet computer all showed stable output values with an error of within 1%.

Fig. 9(c) shows the ideal output value for the values obtained experimentally, with an output voltage of 100 A to 2.5 V at different rated currents, while varying the temperature between −10 ^oC and 85 ^oC. The value of the overall measurement error is shown in the graph; the higher the output reference temperature interval, the greater the rate of change in the corrected width of the compensation value than that in the other temperature segments.