CN112784514B - Equivalent circuit-based modeling method for nano gas sensor - Google Patents
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Abstract
The invention provides a modeling method of a nano gas sensor based on an equivalent circuit, and relates to the technical field of gas sensors. The method comprises the steps of carrying out blind box processing and modularized processing on the nano gas sensor, simulating the nano gas sensor by using an equivalent circuit, packaging the equivalent circuit of the whole nano gas sensor, generating an input and output effect similar to that of an actual sensor, carrying out preliminary division on functions in modularized processing, carrying out module refinement on different parameters, different operation processes and different expression forms, dividing the equivalent circuit into an input circuit subsystem, a conversion circuit subsystem and a filter circuit subsystem, and connecting the three subsystems in series in sequence. The invention solves the problems that the model of the nano gas sensor can only be described but can not be simulated in the process of establishing the model of the nano gas sensor, solves the problem that the model of the nano gas sensor has no universality and simultaneously describes the influence of different parameter changes on the response of the sensor, thereby reducing the cost and improving the efficiency.
Description
Technical Field
The invention relates to the technical field of gas sensors, in particular to a modeling method of a nano gas sensor based on an equivalent circuit.
Background
The gas sensor is a device capable of converting information such as a component and a concentration of a gas into an electric signal, and includes various types such as a semiconductor gas sensor, an electrochemical gas sensor, a catalytic combustion gas sensor, a thermal conductivity gas sensor, an infrared gas sensor, and a solid electrolyte gas sensor.
In recent years, gas sensors have been widely developed in biology, chemistry, machinery, aviation, military and the like, and nanostructured materials have been widely used for manufacturing gas sensors due to advantages of being able to reduce working temperature and consuming less energy, and when the materials reach nanoscale, the properties tend to be suddenly changed. The most important feature of the nanostructured material is a particularly high specific surface area, which will facilitate a sufficient contact between the detection layer of the sensor and the detected gas, thus enhancing the sensitivity of the sensor.
In the aspect of model calculation, the physical mathematical model aiming at the semiconductor metal oxide sensor is not unified all the time, and related theories are numerous. On one hand, the mass transfer sensitivity mechanism inside the sensor for guiding modeling is not clear, on the other hand, the gas sensor has a plurality of materials and a plurality of gases to be detected, and a modeling method with universality is difficult to find through a physical modeling method.
Currently, modeling of nano gas sensors is mostly based on the fact that the response process to gas-sensitive materials at different angles is described by formulas, rather than modeling by building equivalent models. Therefore, although we can obtain a more definite response mechanism of the nano gas sensor as the research is in progress, a simpler representation form cannot be obtained, and the help to the design and production of the actual nano gas sensor is not high. In fact, during the design process of the nano gas sensor, new sensors need to be continuously manufactured and tested to determine the response situation of the nano gas sensor, and during the test process, if only one sample is measured under one condition at a time, a lot of time is spent, and the flow is very complicated. Meanwhile, the common measurement method can only correspond to one specific situation at a time, and if the response capability is required to change along with various variables, the subsequent experimental data processing is quite time-consuming. Therefore, a model building platform with universality is needed, and the design of the sensor can be completed without manufacturing the sensor in a large quantity.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a modeling method of a nano gas sensor based on an equivalent circuit, which replaces environmental variables and parameters inside the sensor with electric signals and utilizes the equivalent circuit to realize the approximate replacement of the response of the sensor in an actual test circuit, thereby reducing the cost and improving the efficiency.
In order to solve the technical problems, the invention adopts the following technical scheme:
a modeling method of a nano gas sensor based on an equivalent circuit comprises the steps of carrying out blind box processing and modularized processing on the nano gas sensor, simulating the nano gas sensor by utilizing the equivalent circuit, packaging the equivalent circuit of the whole nano gas sensor to generate an input and output effect similar to that of an actual sensor, carrying out preliminary division on functions in modularized processing, carrying out module refinement on different parameters, different operation processes and different expression forms, dividing the equivalent circuit into an input circuit subsystem, a conversion circuit subsystem and a filter circuit subsystem, and connecting the three subsystems in series in sequence;
the input circuit subsystem is used for simulating the adsorption and diffusion of the gas on the gas-sensitive material of the nano gas sensor, namely, the gas input process in the actual test process is simulated by inputting an electric signal, and the electric signal with equivalent gas concentration is generated and is output by the output end of the input circuit subsystem and then enters the conversion circuit subsystem through the input port of the conversion circuit subsystem;
the conversion circuit subsystem is used for converting equivalent electric signals of gas concentration, which are transmitted by the input circuit subsystem, into sensor response equivalents and outputting the sensor response equivalents to the filter circuit, under the condition that the Philippine law is suitable for surface reaction of a porous gas sensing material, and experimental gas follows Freund's law in the gas adsorption process, converting parameters which can affect different gas-sensitive characteristics into adjustable electric signals by utilizing a multistage operation circuit according to a diffusion reaction equation of gas and a relation between the electric conduction of a gas-sensitive film and the gas concentration, calculating according to the formula, simulating the sensing characteristic of the whole nano gas sensor, and outputting a result generated by the multistage operation to the filter circuit subsystem; wherein, the diffusion reaction equation of the gas is:
wherein C is the volume concentration of the diffusion gas; t is diffusion time; x is the diffusion distance; d is a diffusion coefficient, and is theoretically a second-order tensor containing 9 components, and is closely related to the structural symmetry of a diffusion system; gamma takes a value of 1 under the condition of small-range coverage;
upon injection of gas within the closed vessel, the equation becomes:
wherein Γres is the response time, Γb is the recovery time, and iota is the film thickness; c (C) 0 D for the concentration of the gas to be measured in the air at the beginning of diffusion e A diffusion coefficient for a gas sensitive material of the sensor;
the filter circuit subsystem is provided with adjustable bandwidth and cut-off frequency, calculates corresponding frequency according to the estimated response-recovery time, sets the bandwidth and cut-off frequency according to the frequency, filters out complex noise generated in the operation process, leaves response waveforms which are suitable for subsequent processing and are close to the response of an actual sensor, and outputs the response waveforms from an output port of the filter circuit subsystem to the oscilloscope.
Further, in the input circuit subsystem, the concentration of the gas to be detected diffused in the gas-sensitive material is equivalent in the circuit structure to be a main independent variable which causes the analog response of the next circuit; the method comprises the steps that an alternating-current voltage source is equivalently used as a variable gas concentration signal, the amplitude voltage of the alternating-current voltage source represents the maximum value of gas concentration, the frequency of the voltage change of the alternating-current voltage source represents the speed of the gas concentration change, and the alternating-current voltage source is connected into an operational amplification circuit for processing, so that the gas concentration signal change output from an input circuit subsystem is consistent with the form of the actual gas concentration change;
in the course of coarse testing, directly using controlled adjustable signal source to replace input circuit; when a specific sensor is simulated, designing according to whether a concentration change process in actual diffusion of gas has an equivalent elementary function model or not; if the equivalent elementary function model exists, the signal source for generating the elementary function type signal is directly utilized to simulate the generation of the signal; if the gas sensor has a unique response rule, the operation amplification processing is carried out on a certain basic function signal according to the response rule of the gas sensor, so that the effect approximately equivalent to the diffusion process occurring on the gas sensitive material of the original gas sensor is achieved.
Further, in the conversion circuit subsystem, parameters which are irrelevant to each other except the diffusion concentration transmitted by the input circuit subsystem are respectively generated by circuit elements or circuit modules which are not affected by each other, and structures are respectively designed according to response changes of the circuit elements or the circuit modules; for partial parameters which are kept unchanged and have no change on the influence of the signal in the actual sensing process, the partial parameters are equivalent by using a capacitor, a resistor and a signal source; parameters which have more complex influence on the sensing process are given by an equivalent circuit branch network; the coupling between circuit elements or circuit modules corresponding to different parameters is realized by an operation circuit according to a gas diffusion reaction equation, the common influence of a plurality of variables which are in direct proportion or inverse proportion to a response result under the same condition on the circuit is converted into the same signal by a four-quadrant multiplication circuit, the influence of different variables is accumulated by addition operation, finally the influence of time accumulation on the response result is obtained by an integration circuit, and the result generated by multi-stage operation is output to a filter circuit subsystem.
Further, macroscopic changes generated by a certain characteristic of the nano gas sensor are actually caused by a plurality of microscopic changes, and the influence of each microscopic change in the sensor caused by the certain characteristic change on an output signal is equivalent to one branch of the branch network, the branches are mutually coupled to form a branch network, and after the gas concentration signal transmitted by an input circuit subsystem is processed together, a result similar to the response of the certain characteristic of the actual sensor is output; adding a delay device into a single branch to simulate the speed of different microscopic changes; a voltage-controlled resistor is added in each branch, the intensity of different microscopic processes is simulated through different piezoresistive ratios, and voltage signals are converted into resistance signals.
The beneficial effects of adopting above-mentioned technical scheme to produce lie in: the modeling method of the nano gas sensor based on the equivalent circuit provided by the invention utilizes the equivalent circuit to simulate the nano gas sensor, and can replace environmental variables and parameters in the sensor by using electric signals, so that only key parameters of the sensor and environmental parameters with larger influence are needed to be obtained, the equivalent circuit can be utilized to realize the approximate replacement of the response of the sensor in an actual test circuit, the problem that the nano gas sensor can only be described but not be simulated in the model building process of the nano gas sensor is solved, the problem that the nano gas sensor model does not have universality and the problem that the response of the sensor is influenced by different parameter changes are simultaneously described, thereby reducing the cost and improving the efficiency.
Drawings
FIG. 1 is a schematic diagram of a nano-gas sensor; wherein, (a) is a front view, (b) is a left view, and (c) is a top view;
fig. 2 is a schematic diagram of an overall structure of an equivalent circuit according to an embodiment of the present invention;
FIG. 3 is a circuit configuration diagram of an input circuit subsystem according to an embodiment of the present invention;
FIG. 4 is a circuit configuration diagram of a conversion circuit subsystem according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of an equivalent circuit of a single effect of temperature on a sensing process according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of an equivalent circuit network in which temperature affects a sensing process according to an embodiment of the present invention;
fig. 7 is a circuit configuration diagram of a filtering circuit subsystem according to an embodiment of the present invention.
In the figure: 1. a base; 2. a sensor lower pin; 3. a ceramic tube; 4. a resistance wire; 5. a pin on the sensor; 6. and (5) a lead wire.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
The present embodiment performs model simulation on the nano gas sensor as shown in fig. 1. In the nano gas sensor, the gas sensitive material is diluted and then uniformly coated on the surface of a ceramic tube, a resistance wire is placed in the ceramic tube, and finally two ends of the resistance wire and four pins of the ceramic tube are welded with a base. By changing the voltage across the wire, the power of the wire is changed to change the temperature, and the response of the material to the gas is reflected from the change in the output current.
The response performance of a nano-gas sensor is affected by a number of factors. Under the condition that other conditions are unchanged, the sensors of different gas-sensitive materials have different response capacities even under the same gas environment, and the response capacities of the same sensor for different concentrations of the gas to be measured are different. In addition, temperature variations can also affect the response capability of the sensor.
Therefore, in the design process of the sensor model, the gas-sensitive material parameter, the gas parameter to be detected, the concentration of the gas to be detected and the working temperature of the sensor are required to be respectively converted into signals, so that a result similar to the response of an actual sensor is obtained. In order to make the designed equivalent model universal, each parameter influencing the sensor response must be adjustable to simulate the response process of different materials, different gases to be tested and different environments. The method for simulating the nano gas sensor by the equivalent circuit in the embodiment selects the electric signals as equivalent signals of all parameters and variables in the sensor response process, and can simulate the actual response of the sensor under the condition that the form and the size of the electric signals are changed by changing the circuit structure and the element parameters so as to freely represent the change of all the parameters.
In this embodiment, the nano gas sensor is subjected to blind box processing and modularized processing, that is, after the whole nano gas sensor equivalent circuit is packaged, an input and output effect similar to that of an actual sensor is generated, while the modularized processing is performed by initially dividing functions, and then refining modules of different parameters, different operation processes and different expression forms, so that the simulation process is reasonable.
The embodiment specifically provides a modeling method of a nano gas sensor based on an equivalent circuit, which comprises the steps of simulating the nano gas sensor by using the equivalent circuit in a design process, dividing the equivalent circuit of the nano gas sensor into three subsystems of an input circuit, a conversion circuit and a filter circuit, sequentially connecting the three subsystems in series, outputting a gas concentration equivalent electric signal generated by the input circuit subsystem by an output end of the input circuit subsystem, entering the conversion circuit subsystem through an input port of the conversion circuit, processing by the conversion circuit, outputting the gas concentration equivalent electric signal from an output port of the conversion circuit to an input port of the filter circuit, modifying a waveform by the filter circuit, and outputting the waveform from the output port of the filter circuit to an oscilloscope. The overall coupling mode between the subsystems is shown in fig. 2, and the function and design method of each subsystem are as follows.
Fig. 3 is a schematic circuit diagram of an input circuit subsystem for simulating adsorption and diffusion of gas on a gas-sensitive material of a nano-gas sensor, and the concentration of the gas to be measured diffused in the gas-sensitive material is equivalent in the circuit structure to be a main independent variable for causing the generation of a subsequent electrical analog response. The alternating voltage source is connected to the operational amplifying circuit for processing, so that the gas concentration signal output from the input circuit subsystem changes in a consistent manner with the actual gas concentration change. In the course of coarse test, the controlled adjustable signal source can be directly used to replace input circuit, when a specific sensor is simulated, according to the fact that the concentration change process in the actual diffusion of gas has an equivalent elementary function model or not, if the equivalent elementary function model is provided, the signal source for generating the functional signal can be directly used to simulate the generation of the signal, if the unique response rule is provided, the operational amplification processing is carried out on a certain basic function signal according to the response rule of the signal source, so that the effect approximately equivalent to the diffusion process occurring on the gas-sensitive material of the original gas sensor is achieved, and in fig. 3, the alternating voltage source is connected to the secondary operational amplification circuit to represent the process. The concentration change signal generated by the input circuit is output from the output port of the input circuit subsystem and then enters the conversion circuit.
Fig. 4 is a schematic circuit diagram of a converting circuit subsystem for calculating a gas concentration signal inputted from an input circuit by using a multistage operation circuit according to a relation between a diffusion reaction equation of gas and the conductance and gas concentration of a gas-sensitive film, and obtaining an output signal similar to an actual sensor response. The diffusion reaction equation of the gas is:
wherein, C is the volume concentration of the diffusion gas, t is the diffusion time, and x is the diffusion distance. The diffusion coefficient D is theoretically a second order tensor with 9 components, and is closely related to the structural symmetry of the diffusion system. Gamma takes a value of 1 in the case of small range coverage.
Upon injection of gas within the closed vessel, the equation becomes:
wherein Γres is the response time, Γb is the recovery time, and iota is the film thickness; c (C) 0 D for the concentration of the gas to be measured in the air at the beginning of diffusion e Is the diffusion coefficient of the gas-sensitive material of the sensor.
The independent variables except the diffusion concentration are respectively generated by circuit elements or circuit modules which are not mutually influenced, and the structures are respectively designed according to the corresponding changes of the independent variables.
Meanwhile, among various parameters affecting the response of the sensor, the working temperature of the sensor is special, the sensor is complex in influence on the sensing process, the macroscopic change of the nano gas sensor due to the temperature characteristic is actually caused by a plurality of microscopic changes, and the macroscopic change comprises oxygen ion adsorption, electron adsorption, transition and oxidation heat release processes, so that the embodiment utilizes the influence of the equivalent circuit branch network simulation temperature characteristic on the response process of the nano gas sensor. In the embodiment, the alternating current voltage source is used for representing temperature change, the voltage amplitude represents the temperature, and the frequency represents the speed of temperature change. The motion degree of electrons in different temperature ranges in the microscopic process, namely the sensitivity of the sensor, is also different, so a delay device L1 is added in a single branch to simulate the speed of different microscopic changes. The intensity of different micro-responses is also different, so that a voltage-controlled resistor U1 is added in the circuit, the intensity of different micro-processes is simulated through different piezoresistive proportions, and a voltage signal is converted into a resistance signal. The influence of each microscopic change caused by temperature change in the sensor on the output signal is equivalent to one branch of the circuit, and the branches are coupled with each other as shown in fig. 5, so that the branch network shown in fig. 6 is formed to process the temperature signal together, and then a result similar to the temperature response of the actual sensor is output. In the integrated analog circuit, two output ends of the branch network, namely, two ports connected with the oscilloscope are respectively connected with the positive end and the negative end of the IO2 in fig. 4, so that a temperature signal is introduced into the operation of the integrated analog circuit.
The diffusion reaction equation of the coupling reference gas among different parameter analog circuits is realized by an operation circuit, the common influence of a plurality of variables which are in direct proportion or inverse proportion to the response result under the same condition on the circuit is converted into the same signal by a four-quadrant multiplication circuit, the influence of different variables is mutually accumulated by addition operation, finally the influence of time accumulation on the response result is obtained by an integration circuit, and the result generated by multi-stage operation is output to a filter circuit.
Fig. 7 is a schematic circuit diagram of a filtering circuit subsystem, and the filtering circuit is used for filtering the electric signal obtained by the conversion circuit to leave a smoother signal waveform which is easy to analyze. The designed filter circuit has adjustable bandwidth and cutoff frequency, is a structure of a band-pass filter, calculates corresponding frequency according to the estimated response-recovery time in the specific equivalent circuit design process, sets the bandwidth and the cutoff frequency according to the frequency, filters out complex noise generated in the operation process, and leaves an output waveform which is suitable for subsequent processing and is close to the actual sensor response. The processed signal output from the filter circuit can be connected to an oscilloscope like a normal gas sensor, and the response result is observed.
The specific simulation flow of the equivalent circuit example of the nano gas sensor designed by the embodiment is as follows: the input circuit uses the group alternating current voltage source signals to obtain equivalent circuit signals which approximately replace the change of the gas concentration through the secondary operational amplification processing; in the conversion circuit, combining formulas, and simulating the processes of gas-sensitive film adsorption and response to the concentration change of the gas to be detected by utilizing the coupling of the coupling circuit of the operation circuit, wherein except that the concentration signal of the gas to be detected is provided by the input circuit, each parameter which is not affected by each other is provided by different circuit elements or circuit modules respectively; and after the signal output by the conversion circuit is processed by the filter circuit, the obtained circuit signal is transmitted to the oscilloscope for observation.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions, which are defined by the scope of the appended claims.
Claims (3)
1. A modeling method of a nano gas sensor based on an equivalent circuit is characterized by comprising the following steps of: the method comprises the steps of carrying out blind box processing and modularized processing on a nano gas sensor, simulating the nano gas sensor by using an equivalent circuit, packaging the equivalent circuit of the whole nano gas sensor, generating an input and output effect similar to that of an actual sensor, carrying out preliminary division on functions in modularized processing, carrying out module refinement on different parameters, different operation processes and different expression forms, dividing the equivalent circuit into an input circuit subsystem, a conversion circuit subsystem and a filter circuit subsystem, and connecting the three subsystems in series in sequence;
the input circuit subsystem is used for simulating the adsorption and diffusion of the gas on the gas-sensitive material of the nano gas sensor, namely, the gas input process in the actual test process is simulated by inputting an electric signal, and the electric signal with equivalent gas concentration is generated and is output by the output end of the input circuit subsystem and then enters the conversion circuit subsystem through the input port of the conversion circuit subsystem; in the input circuit subsystem, the concentration of the gas to be detected diffused in the gas-sensitive material is equivalent in a circuit structure to be a main independent variable which causes the analog response of the next circuit; the method comprises the steps that an alternating-current voltage source is equivalently used as a variable gas concentration signal, the amplitude voltage of the alternating-current voltage source represents the maximum value of gas concentration, the frequency of the voltage change of the alternating-current voltage source represents the speed of the gas concentration change, and the alternating-current voltage source is connected into an operational amplification circuit for processing, so that the gas concentration signal change output from an input circuit subsystem is consistent with the form of the actual gas concentration change;
in the course of coarse testing, directly using controlled adjustable signal source to replace input circuit; when a specific sensor is simulated, designing according to whether a concentration change process in actual diffusion of gas has an equivalent elementary function model or not; if the equivalent elementary function model exists, the signal source for generating the elementary function type signal is directly utilized to simulate the generation of the signal; if the gas sensor has a unique response rule, carrying out operational amplification processing on a certain basic function signal according to the response rule of the gas sensor, so as to achieve the effect approximately equivalent to the diffusion process occurring on the gas sensitive material of the original gas sensor;
the conversion circuit subsystem is used for converting equivalent electric signals of gas concentration, which are transmitted by the input circuit subsystem, into sensor response equivalents and outputting the sensor response equivalents to the filter circuit, under the condition that the Philippine law is suitable for surface reaction of a porous gas sensing material, and experimental gas follows Freund's law in the gas adsorption process, converting parameters which can affect different gas-sensitive characteristics into adjustable electric signals by utilizing a multistage operation circuit according to a diffusion reaction equation of gas and a relation between the electric conduction of a gas-sensitive film and the gas concentration, calculating according to the formula, simulating the sensing characteristic of the whole nano gas sensor, and outputting a result generated by the multistage operation to the filter circuit subsystem; wherein, the diffusion reaction equation of the gas is:
wherein C is the volume concentration of the diffusion gas; t is diffusion time; x is the diffusion distance; d is a diffusion coefficient, and is theoretically a second-order tensor containing 9 components, and is closely related to the structural symmetry of a diffusion system; gamma takes a value of 1 under the condition of small-range coverage;
upon injection of gas within the closed vessel, the equation becomes:
wherein Γres is the response time, Γb is the recovery time, and iota is the film thickness; c (C) 0 D for the concentration of the gas to be measured in the air at the beginning of diffusion e A diffusion coefficient for a gas sensitive material of the sensor;
the filter circuit subsystem is provided with adjustable bandwidth and cut-off frequency, calculates corresponding frequency according to the estimated response-recovery time, sets the bandwidth and cut-off frequency according to the frequency, filters out complex noise generated in the operation process, leaves response waveforms which are suitable for subsequent processing and are close to the response of an actual sensor, and outputs the response waveforms from an output port of the filter circuit subsystem to the oscilloscope.
2. The equivalent circuit-based nano-gas sensor modeling method of claim 1, wherein: in the conversion circuit subsystem, parameters which are irrelevant to each other except the diffusion concentration transmitted by the input circuit subsystem are respectively generated by circuit elements or circuit modules which are not affected by each other, and structures are respectively designed according to response changes of the circuit elements or the circuit modules; for partial parameters which are kept unchanged and have no change on the influence of the signal in the actual sensing process, the partial parameters are equivalent by using a capacitor, a resistor and a signal source; parameters which have more complex influence on the sensing process are given by an equivalent circuit branch network; the coupling between circuit elements or circuit modules corresponding to different parameters is realized by an operation circuit according to a gas diffusion reaction equation, the common influence of a plurality of variables which are in direct proportion or inverse proportion to a response result under the same condition on the circuit is converted into the same signal by a four-quadrant multiplication circuit, the influence of different variables is accumulated by addition operation, finally the influence of time accumulation on the response result is obtained by an integration circuit, and the result generated by multi-stage operation is output to a filter circuit subsystem.
3. The equivalent circuit-based nano-gas sensor modeling method of claim 2, wherein: the macroscopic change of the nano gas sensor due to a certain characteristic is actually caused by a plurality of microscopic changes, and the influence of each microscopic change of the sensor due to the certain characteristic change on an output signal is equivalent to one branch of the branch network, the branches are mutually coupled to form a branch network, and after the gas concentration signal transmitted by an input circuit subsystem is processed together, a result similar to the response of the certain characteristic of the actual sensor is output; adding a delay device into a single branch to simulate the speed of different microscopic changes; a voltage-controlled resistor is added in each branch, the intensity of different microscopic processes is simulated through different piezoresistive ratios, and voltage signals are converted into resistance signals.
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| JPH11132996A (en) * | 1997-08-27 | 1999-05-21 | Denso Corp | Element resistance detection method of oxygen concentration sensor |
| EP0942281A2 (en) * | 1998-03-13 | 1999-09-15 | Siemens Aktiengesellschaft | Measuring circuit for determining the concentration of one or more gases in a gaseous mixture |
| CN108710774A (en) * | 2018-06-20 | 2018-10-26 | 华中科技大学 | A kind of current sensor frequency characteristic modeling method |
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