WO2014075361A1

WO2014075361A1 - Voltage detection apparatus and method

Info

Publication number: WO2014075361A1
Application number: PCT/CN2012/085726
Authority: WO
Inventors: 龙涛; 刘正东; 龙江; 乔磊; 严松
Original assignee: 江苏惠通集团有限责任公司
Priority date: 2012-11-14
Filing date: 2012-12-03
Publication date: 2014-05-22
Also published as: CN102944717B; CN102944717A

Abstract

A voltage detection apparatus and method. The apparatus comprises: a first terminal (1) and a second terminal (2) which are connected to two ends of a voltage source to be tested (VDD) respectively, a first divider resistor (R201) and a second divider resistor (R202) which are connected in series between the first terminal (1) and the second terminal (2), a detection device (MCU (1)), a reference voltage source, a first arithmetic unit (F1) and a second arithmetic unit (F2). The method includes: enabling the voltage source to be tested (VDD) to suspend working; providing a reference voltage, and according to the resistance values of the first divider resistor (R201) and the second divider resistor (R202) and a first partial voltage value acquired by the detection device (MCU (1)) at this moment, obtaining the internal resistance value of the detection device (MCU (1)); and enabling the voltage source to be tested (VDD) to resume working, and according to the internal resistance value, the resistance values of the first divider resistor (R201) and the second divider resistor (R202) and a second partial voltage value acquired by the detection device (MCU (1)) at this moment, obtaining the voltage value of the voltage source to be tested (VDD).

Description

。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。 BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to voltage detection, and more particularly to an apparatus and method for voltage detection. BACKGROUND OF THE INVENTION With regard to voltage detection, it is conventional to use a device as shown in FIG. 1 including terminal 1 , terminal 2, voltage dividing resistor R101, voltage dividing resistor R102, detection device integrated in MCU (microcontroller) (for example, selecting AD sampling module as the detecting device), detecting device has detecting terminal 3. Terminal 1 and terminal 2 It can be connected to both ends of the voltage source VDD to be tested, and the voltage source VDD to be tested supplies power to the detecting device. As can be seen from Figure 1, the terminal 1 is integrated into the voltage source VDD and the terminal 2 is grounded. The voltage dividing resistor R101 and the voltage dividing resistor R102 are The detection terminal 3 of the detecting device is connected in series between the terminal 1 and the terminal 2 to connect the voltage dividing resistor R101 and the divided piezoelectric The connection node 4 of R102 detects the voltage division value at the connection node 4. The condition of the conventional detection method is approximated according to the voltage division value of the detection device at the connection node 4, the resistance value of the voltage dividing resistor R101 and the voltage dividing resistor R102. The voltage data of the voltage source VDD; can be realized by the following calculation formula:

VDD ^ x ^{101 102}

八102 where VDD is the voltage value of the voltage source to be tested; 3⁄4π is the resistance value of the voltage dividing resistor R101; 2 is the resistance value of the voltage dividing resistor R101; ^ν ι is the voltage dividing value on the connection node 4 when the voltage source VDD to be tested is working. The calculation process of the above calculation formula can be implemented by the MCU. The inventors have found that the conventional voltage detection method has at least the following two problems: 1. The resistance value of the voltage dividing resistor R101 and the voltage dividing resistor R102 needs to be set to a small value, so that the above detection result is more accurate, and the partial pressure is When the resistance is set to a large value, the accuracy is very low. 2. Since the resistance of the voltage dividing resistor R101 and the voltage dividing resistor R102 is small, the power consumption consumed during the detection process is large, and generally only applicable to low power consumption. In the case of the request, the application is limited. Chinese Patent Application Publication No. CN1379301 discloses a voltage detecting circuit on November 13, 2002, which mainly includes the following: a voltage divider including a pair of resistors connected in series; a comparator having a connection to the divided voltage A positive input terminal in the middle of the device, a negative input terminal connected to the reference voltage circuit, and an input terminal connected to an external terminal that controls the comparator to be turned on and off; a buffer circuit connected to the output terminal of the comparator. The problem solved is how to reduce the current consumption in the voltage detecting circuit and improve the response speed of the comparator in the voltage detecting circuit. There is no technical solution to solve the above problems. SUMMARY OF THE INVENTION The technical problem solved by the application of the present invention is how to achieve arbitrary selection of the resistance of the voltage dividing resistor while ensuring the accuracy of the voltage detection. In order to solve the above technical problem, the present invention provides a voltage detecting device including a first voltage dividing resistor connected between a first terminal and a second terminal, and a series connection between the first terminal and the second terminal, respectively, to the two ends of the voltage source to be tested. And a second voltage dividing resistor and a detecting device for obtaining a voltage dividing value at a connection node of the first voltage dividing resistor and the second voltage dividing resistor, the voltage detecting device further comprising: a reference voltage source, when the voltage source to be tested is suspended, The first terminal is configured to supply power to the detecting device by using the first terminal, and the first computing unit is configured to: when the reference voltage source is operated, the first voltage dividing value, the first voltage dividing resistor, and the second voltage dividing resistor obtained by the detecting device Obtaining an internal resistance value of the detecting device; and a second operation unit, configured to: when the voltage source to be tested operates, the second partial pressure value obtained by the detecting device, the internal resistance value, and the first voltage dividing resistor and the second component The resistance of the voltage resistor is obtained as the voltage value of the voltage source to be tested. Optionally, a sum of resistances of the first voltage dividing resistor and the second voltage dividing resistor is greater than an internal resistance value of the detecting device. Optionally, the first operation unit is configured to implement the following calculation formula:

_R _ RR U,

i ⁿ ~ VCC x R ₂ - R, x U, - R ₂ x U, where R _in is the internal resistance of the detecting device; is the resistance of the first voltage dividing resistor; ^ is the resistance of the second voltage dividing resistor a value; ^ is the first divided voltage value; VCC is a voltage value of the reference voltage source. Optionally, the second operation unit is configured to implement the following calculation formula:

R ₇ X R.

R, ——≡~

R, + R.

VDD = U, X -

R ₂ + R _in where VDD is the voltage value of the voltage source to be tested; A is the resistance value of the first voltage dividing resistor; R ₂ is the resistance value of the second voltage dividing resistor; R _in is the internal resistance value of the detecting device; U ₂ is the second partial pressure value. Optionally, the resistance values of the first voltage dividing resistor and the second voltage dividing resistor may be previously written into the first arithmetic unit and the second computing unit. Optionally, the first operation unit and the second operation unit are implemented by an MCU chip. Optionally, the detecting device is also integrated on the MCU chip. In order to solve the above technical problem, the present invention further provides a voltage detecting method for obtaining a voltage value of a voltage source to be tested, and a first voltage dividing resistor and a second voltage dividing resistor are disposed between two ends of the voltage source to be tested. Obtaining a detection device for dividing the voltage on the connection node of the first voltage dividing resistor and the second voltage dividing resistor, the voltage detecting method includes: suspending the voltage source to be tested; providing a reference voltage according to the first voltage dividing resistor and the first The resistance value of the bipartite resistor and the first voltage division value obtained by the detecting device at this time, the internal resistance value of the detecting device is obtained; the voltage source to be tested is restored to work according to the internal resistance value, the first voltage dividing resistor and the first The resistance of the voltage divider resistor and the second voltage divider value obtained by the detecting device at this time obtain the voltage value of the voltage source to be tested. The beneficial effects of the above technical solution include at least: obtaining an internal resistance value R _in of the detecting device by first providing a reference voltage to the detecting device (provided by the reference voltage source in the device); and then according to the internal resistance value R _in , the first partial voltage The resistance value of the resistor and the second voltage dividing resistor and the voltage dividing value obtained by the detecting device at the connection node obtain the real-time voltage value of the voltage source to be tested, thereby improving the accuracy of the voltage detection.

The first voltage dividing resistor and the second voltage dividing resistor of any resistance range can be applied, and the device for detecting low power demand can be adapted and has a wide application range. In particular, it is preferable to have a large resistance voltage dividing resistor Low-power measurement of current voltage,

1 is a schematic structural view of a voltage detecting device in the prior art;

2 is a schematic structural diagram of a voltage detecting device according to an embodiment of the present invention;

FIG. 3 is a schematic flow chart of a voltage detecting method according to an embodiment of the present invention.

detailed description

It can be seen from the background art of the present application that the conventional voltage detection method adopts the voltage detecting device shown in FIG. 1 , because the voltage division of the connection node 4 obtained by the detecting device is equivalent to the voltage on the voltage dividing resistor R102, and then Through the calculation formula:

The instantaneous voltage data of the voltage to be tested VDD is obtained. Where VDD is the voltage value of the voltage source VDD to be tested in Figure 1, R _{1 (n} is the resistance value of the voltage dividing resistor R101, ₂ is the resistance value of the voltage dividing resistor R102, 1⁄4 is the detecting device from the voltage source VDD when operating The partial pressure value obtained by the connection node 4. However, according to the inventor's analysis: The partial pressure value at the connection node 4 indicated by the formula 1 means that the terminal 1 is connected in series with

Voltage: Set the voltage value to have:

V, = VDDx-

(R _im + R, but the voltage value of Equation 2 is actually an equivalent partial pressure value instead of the actual partial pressure value: When detecting this voltage, it means that the detection terminal 3 of the detecting device acquires the partial pressure of the connection node 4 Equation 2 does not consider the internal resistance value at the port of the detection device detection terminal 3: the partial voltage value at the actual connection node 4 is v ₂ , which is: xR.

+ R.

V, = VDDx-

R, xR _; ,

R + R;, Comparing Equations 2 and 3, the conventional voltage detection method needs to make ^ » R ₁₀₁ + R ₁₀₂ when selecting the resistance of the voltage dividing resistor, so that the voltage dividing value V ₂ at the actual connection node 4 (considering the internal resistance of the detecting device) Value) Equivalent to ignoring the voltage value across the second voltage dividing resistor when detecting the internal resistance of the device, directly calculating the VDD through the resistance conversion of the first voltage dividing resistor and the second voltage dividing resistor (ie, the process of Equation 1). Although the above algorithm can achieve the purpose of fast detection, this method has low resistance value of the voltage dividing resistor and high power consumption of the circuit; for different types and types of detecting devices, R _in is often non-constant value, voltage detection The voltage measured by the device has a large difference from the true value, and the voltage detection accuracy is low. It is considered that the voltage dividing value on the node 4 connected by the voltage dividing resistor R101 and the voltage dividing resistor R102 obtained by the detecting device is equivalent to the voltage value across the voltage dividing resistor R102 when the internal resistance value of the detecting device is ignored, resulting in the voltage dividing resistor. The value range is limited and cannot meet the technical problems of voltage detection involved in the low-power devices, such as the background art. Therefore, the present embodiment provides a voltage detection based on the internal resistance of the detecting device. Device and voltage detection method. A voltage detecting device as shown in FIG. 2 is for detecting an instantaneous voltage of a voltage source VDD to be tested. The voltage source VDD to be tested supplies power to the detecting device, wherein the detecting device is integrated in an MCU chip, which is the MCU (1) in the figure. Port 3 of the MCU ( 1 ) is the AD port that detects the device detection terminal. The detection device can be an AD sampling module. The voltage detecting device of FIG. 2 includes a first voltage dividing resistor R201 and a first terminal connected to the voltage source VDD to be tested, respectively, a first terminal 1, a second terminal 2, and a series connection between the first terminal 1 and the second terminal 2; The voltage dividing resistor R202, the detecting terminal 3 of the detecting device is connected to the connecting node 4 of the first voltage dividing resistor R201 and the second voltage dividing resistor R202 to obtain a voltage dividing value. Specifically, the first terminal 1 is connected to the voltage source VDD to be tested, and the second terminal is connected to the ground GND; one end of the first voltage dividing resistor R201 is connected to the voltage source VDD to be tested, and the other terminal is connected to the second voltage dividing resistor R202; One end of the voltage resistor R202 is respectively connected to the first voltage dividing resistor R201 and the detecting terminal 3 of the detecting device, and the other end is connected to the ground GND; the first voltage dividing resistor R201 is connected to the end of the voltage source VDD to be tested, which is the first terminal 1, The ground terminal of the second voltage dividing resistor R202 is the second terminal 2. In this embodiment, the sum of the resistance values of the first voltage dividing resistor R201 and the second voltage dividing resistor R202 may be selected to be greater than the internal resistance value Rin of the detecting device. Since the approximate range of the internal resistance value Rin of the detecting device is generally estimable, the resistance values of the first voltage dividing resistor R201 and the second voltage dividing resistor R202 are also estimable, and can be selected within a known range, and The structure of the voltage detecting device is set. Select a large value divider resistor full The detection requirements of low power circuits are sufficient. The voltage detecting device in FIG. 2 further includes: a reference voltage source (not specifically labeled in the figure, which may be set in the first operation unit F1, or may be separately set; its function is independent), and the voltage source VDD to be tested is suspended. The reference voltage source supplies power to the detecting device through the first terminal 1; the first computing unit F1 is configured to: when the reference voltage source operates, according to the first voltage dividing value acquired by the detecting device, the first voltage dividing resistor R201 and the second The resistance value of the voltage dividing resistor R202 is obtained by the internal resistance value Rin of the detecting device; the internal resistance value Rin is the equivalent input internal resistance at the detecting device detecting terminal 3; the first voltage dividing value is the detecting device when the reference voltage source is operated The relative potential on the connection node 4 detected on the terminal 3 is detected. The first operation unit F1 is used to implement the following calculation formula:

R, x R, χ [/,

VCC x R, - R, x [/, - R x U, where R _in is the internal resistance of the sensing device; is the resistance of the first voltage dividing resistor R201; R ₂ is the resistance of the second voltage dividing resistor R202 Value; is the first voltage divider value; VCC is the voltage value of the reference voltage source. The second operation unit F2 is configured to: when the voltage source to be tested is operated, obtain the second partial pressure value, the internal resistance value Rin, and the resistance values of the first voltage dividing resistor R201 and the second voltage dividing resistor R202 obtained by the detecting device, The voltage value of the voltage source to be tested. The following calculation formula is implemented in the second operation unit F2:

_R , ₊ ^RR '

VDD = U, x- ^{R + R;} '

Where VDD is the voltage value of the voltage source to be tested; is the resistance value of the first voltage dividing resistor R201; R ₂ is the resistance value of the second voltage dividing resistor R202; R _in is the internal resistance value of the detecting device; U ₂ is the The second partial pressure value is described. In one embodiment, as shown in FIG. 2, the second computing unit F2 may include the following two units, namely a ratio output unit and a multiplier. Ratio output unit, used for the internal resistance value Rin obtained by the first operation unit F1, the first partial piezoelectric The resistance values of the resistor R201 and the second voltage dividing resistor R202 are obtained as a ratio of the voltage value of the reference voltage source to the first voltage dividing value; the ratio is the same as the ratio of the voltage value of the voltage source to be tested and the second voltage dividing value. The above ratio output unit can be specifically implemented by the following calculation formula:

Where k is the ratio of the voltage value of the reference voltage source to the first voltage dividing value; the resistance value of the first voltage dividing resistor; R ₂ is the resistance value of the second voltage dividing resistor; R _in is the inside of the detecting device Resistance value. The multiplier is configured to multiply and output the second divided value detected by the detecting device and the ratio output by the second arithmetic unit F2 when the voltage source VDD to be tested is operated. The second divided voltage value is a relative potential on the connection node 4 when the voltage source VDD to be tested is operating. For the device structure, the resistance values of the first voltage dividing resistor R201 and the second voltage dividing resistor R202 can be written into the first computing unit F1 and the second computing unit F2 in advance, and the first computing unit F1 and the second The arithmetic unit F2 is implemented by an MCU chip (the first arithmetic unit F1 and the second arithmetic unit F2 are integrated on the MCU (2) chip in FIG. 2). In other embodiments, the detecting device, the first computing unit F1, and the second computing unit F2 may be integrated on the same chip. A voltage detecting method as shown in FIG. 3 for obtaining a voltage value of a voltage source to be tested can be realized by using a voltage detecting device as shown in FIG. 2. A first voltage dividing resistor, a second voltage dividing resistor, and a detecting device for obtaining a voltage dividing value on the connection node of the first voltage dividing resistor and the second voltage dividing resistor are disposed between the two ends of the voltage source to be tested, including:

S1: suspending the voltage source to be tested; S2: providing a reference voltage and obtaining the inside of the detecting device according to the resistance values of the first voltage dividing resistor and the second voltage dividing resistor and the first partial pressure value obtained by the detecting device at this time Resistance value; can be achieved by the following calculation formula:

Wherein, R _in is the internal resistance value of the detecting device; is the resistance value of the first voltage dividing resistor; ^ is the second point The resistance of the voltage resistor; ^ is the first voltage division value; VCC is the reference voltage. The reference voltage can be provided by a reference voltage source. If the voltage detecting device shown in FIG. 2 is used for voltage detection, when the reference voltage source is operated, the internal resistance value Rin of the detecting device can be calculated according to the first partial voltage value on the connecting node 4 obtained by the detecting device detecting terminal 3; After the internal resistance value Rin is obtained by using the first operation unit F1 in FIG. 2, the internal resistance value Rin can be written into the first operation unit F1 for recording (the value is a constant value), and the internal resistance value can be directly output without recording. Rin to the second operation unit F2, the internal resistance value is written into the first operation unit F1, so that the user can extract and display the internal resistance value at any time;

S3: returning the voltage source to be tested and obtaining the voltage source to be tested according to the internal resistance value, the resistance values of the first voltage dividing resistor and the second voltage dividing resistor, and the second partial pressure value obtained by the detecting device at this time. The voltage value can be realized by the following calculation formula:

R, +

VDD = U, x- ^{R + R;} '

Where VDD is the voltage value of the voltage source to be tested; 3⁄4 is the resistance value of the first voltage dividing resistor; R ₂ is the resistance value of the second voltage dividing resistor; R _in is the internal resistance value of the detecting device; U ₂ is the The second partial pressure value. Corresponding to the device shown in FIG. 2, step S3 may further include the following two steps in another embodiment:

S301: performing resistance conversion on the resistance values of the obtained detecting device, the first voltage dividing resistor and the second voltage dividing resistor to obtain a ratio of the voltage value of the reference voltage source to the first partial pressure value; After the ratio output unit of the operation unit F2 obtains the ratio, the ratio can be written into the ratio output unit; when the voltage source VDD to be tested resumes operation, the ratio output unit can directly output the ratio to the multiplier for calculation of the detected voltage. It can be directly output to the multiplier without writing, and recorded by the multiplier.

The ratio of the reference voltage source in S301 to the first partial pressure value can be realized by the following calculation formula:

R + Where k is the ratio of the voltage value of the reference voltage source to the first voltage value; the resistance value of the first voltage dividing resistor; R ₂ is the resistance value of the second voltage dividing resistor; R _in is the internal resistance of the detecting device value.

S302: Resume the operation of the voltage source to be tested, and compare the second partial pressure value obtained by the detecting device at the connection node (connecting node 4) with the ratio obtained in S301 (the ratio of the voltage value of the reference voltage source to the first partial pressure value) Multiply and output; the result of the output is the detection of the instantaneous voltage detection value of the voltage source VDD to be tested. The specific calculation formula is: VDD = U ₂ xk. Step S2 and S301~S302 firstly provide the detection device with the input internal resistance value Rin of the detection terminal port of the reference voltage acquisition detecting device; and further, based on the internal resistance value of the detecting device and the resistance value of the first voltage dividing resistor and the second voltage dividing resistor Converting the ratio of the reference voltage reference source to the voltage dividing value on the connection node 4, since the ratio of the voltage value of the voltage source to be tested to the voltage dividing value on the connection node 4 is a constant value, it is only necessary to record the ratio. When the actual detection is performed, the partial pressure value on the connection node 4 is directly detected, and the partial pressure value is multiplied by the ratio to obtain accurate voltage detection data. Moreover, in the preferred embodiment of the voltage detecting method of the embodiment, in order to realize the low power consumption measurement of the detecting circuit, the resistance of the voltage dividing resistor can be set to be large, 4 R _{1 +} R _{2 >} R _m ; The resistance of the voltage resistor is not limited to this range. The voltage detection method of the present application does not impose any limitation on the resistance range of the voltage divider resistor, and the accurate result of the voltage detection can be achieved. The present invention has been disclosed in the preferred embodiments as described above, but it is not intended to limit the invention, and the present invention may be utilized by the method and technical contents disclosed above without departing from the spirit and scope of the invention. The technical solutions make possible changes and modifications, and therefore, the scope of protection of the technical solutions of the present invention is not deviated from the present invention.

Claims

Rights request

A voltage detecting device comprising: a first voltage dividing resistor and a second voltage dividing resistor connected to a first terminal, a second terminal, and a series connection between the first terminal and the second terminal, respectively, and a voltage source to be tested; a detecting device for obtaining a voltage dividing value on a connection node of the first voltage dividing resistor and the second voltage dividing resistor, further comprising: a reference voltage source, when the voltage source to be tested is suspended, passing the first terminal pair The first operating unit is configured to obtain the internal resistance of the detecting device according to the first partial voltage value, the first voltage dividing resistor and the second voltage dividing resistor obtained by the detecting device when the reference voltage source is operated. a second operation unit, configured to: when the voltage source to be tested operates, according to the second partial pressure value obtained by the detecting device, the internal resistance value, and the resistance values of the first voltage dividing resistor and the second voltage dividing resistor, The voltage value of the voltage source to be tested.

2. The voltage detecting device according to claim 1, wherein a sum of resistances of the first voltage dividing resistor and the second voltage dividing resistor is greater than an internal resistance value of the detecting device.

3. The voltage detecting device according to claim 1, wherein the first arithmetic unit is configured to implement the following calculation formula:

R, X R, χ [/,

FL =

VCC x R, - R, x [/, - R x U, where R _in is the internal resistance of the sensing device; is the resistance of the first voltage dividing resistor; ^ is the resistance of the second voltage dividing resistor; The first voltage dividing value; VCC is a voltage value of the reference voltage source.

4. The voltage detecting device according to claim 1, wherein the second arithmetic unit is configured to implement the following calculation formula:

VDD = U, x- ^{R + R}

Where VDD is the voltage value of the voltage source to be tested; the resistance value of the first voltage dividing resistor; R ₂ is the resistance value of the second voltage dividing resistor; R,. „ is the internal resistance value of the detecting device; U ₂ is the The second partial pressure value is described.

The voltage detecting device according to any one of claims 1 to 4, wherein the resistance values of the first voltage dividing resistor and the second voltage dividing resistor are written in advance to the first arithmetic unit and the first Two arithmetic units.

The voltage detecting device according to any one of claims 1 to 4, wherein the first arithmetic unit and the second arithmetic unit are implemented by an MCU chip.

7. The voltage detecting device according to claim 6, wherein said detecting device is also integrated on said MCU chip.

8. A voltage detecting method for obtaining a voltage value of a voltage source to be tested, wherein a first voltage dividing resistor, a second voltage dividing resistor, and a first voltage dividing resistor are obtained between two ends of the voltage source to be tested The device for detecting the voltage division value at the connection node of the two-dividing resistor, comprising: suspending the voltage source to be tested; providing a reference voltage according to the resistance values of the first voltage dividing resistor and the second voltage dividing resistor; At this time, the first partial pressure value obtained by the detecting device is obtained, and the internal resistance value of the detecting device is obtained; the voltage source to be tested is restored to work and according to the internal resistance value, the resistance values of the first voltage dividing resistor and the second voltage dividing resistor, and At this time, the second partial pressure value obtained by the device is detected, and the voltage value of the voltage source to be tested is obtained.

The voltage detecting method according to claim 8, wherein a sum of resistances of the first voltage dividing resistor and the second voltage dividing resistor is greater than an internal resistance value of the detecting device.

The voltage detecting method according to claim 8, wherein the providing a reference voltage and the first partial pressure obtained by the detecting device according to the resistance values of the first voltage dividing resistor and the second voltage dividing resistor The value of the internal resistance of the detection device is realized by the following calculation formula: i ⁿ YCC x R^ R. x U, - R ₂ x U, where R _in is the internal resistance of the detecting device; Resistance value; ^ is the resistance value of the second voltage dividing resistor; is the first voltage dividing value; VCC is the reference voltage.

The voltage detecting method according to claim 8, wherein the voltage source to be tested is restored to work and according to the internal resistance value, the resistance values of the first voltage dividing resistor and the second voltage dividing resistor, and the like Time check The second partial pressure value obtained by the measuring device obtains the voltage value of the voltage source to be tested by using the following calculation formula:

VDD = U, x- ^{R + R} "

Where VDD is the voltage value of the voltage source to be tested; A is the resistance value of the first voltage dividing resistor; R ₂ is the resistance value of the second voltage dividing resistor; R _in is the internal resistance value of the detecting device; U ₂ is the The second partial pressure value.