CN112710939A - Dynamic stability performance evaluation method of power device - Google Patents

Dynamic stability performance evaluation method of power device Download PDF

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CN112710939A
CN112710939A CN202011504588.6A CN202011504588A CN112710939A CN 112710939 A CN112710939 A CN 112710939A CN 202011504588 A CN202011504588 A CN 202011504588A CN 112710939 A CN112710939 A CN 112710939A
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曾潇
李泽宏
万佳利
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University of Electronic Science and Technology of China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/26—Testing of individual semiconductor devices
    • G01R31/2601—Apparatus or methods therefor
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/26—Testing of individual semiconductor devices
    • G01R31/2607—Circuits therefor
    • G01R31/2608—Circuits therefor for testing bipolar transistors
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/26—Testing of individual semiconductor devices
    • G01R31/2607—Circuits therefor
    • G01R31/2608—Circuits therefor for testing bipolar transistors
    • G01R31/2617—Circuits therefor for testing bipolar transistors for measuring switching properties thereof
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/26—Testing of individual semiconductor devices
    • G01R31/2607—Circuits therefor
    • G01R31/2621—Circuits therefor for testing field effect transistors, i.e. FET's
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/26—Testing of individual semiconductor devices
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    • G01R31/263—Circuits therefor for testing thyristors

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Abstract

The invention relates to a dynamic stability performance evaluation method of a power device, and belongs to the technical field of power devices. The method comprises the steps of obtaining sample data of the power device under different working conditions based on an equivalent circuit of the power device, establishing a state space equation of the power device according to the sample data to obtain a system matrix, and substituting the system matrix into a Lyapunov equation to solve a matrix for judging stability; whether the matrix is positive is judged through Sylvester criterion, whether the power device is stable under different working conditions is obtained, and the instability index of the power device is obtained through counting the number of instability points and stable points, so that whether the power device is stable is judged. The dynamic stability performance of the power device can be judged according to the parameters of the power device in real-time operation, the EMI risk level of the power device is effectively evaluated, the practical application of the power device is favorably guided, reference is provided for the design optimization of the power device, and the scheme has the advantages of simplicity, high efficiency, transportability and the like.

Description

Dynamic stability performance evaluation method of power device
Technical Field
The invention belongs to the technical field of power devices, and particularly relates to a dynamic stability performance evaluation method of a power device.
Background
The power device includes an Insulated Gate Bipolar Transistor (IGBT), a power Metal-Oxide-Semiconductor Field Effect Transistor (MOSFET), a Thyristor, a Gate turn-off Thyristor (GTO), and the like, and is widely applied to various power electronic topologies as a core component of a power electronic technology. With the improvement of the power device design and manufacturing technology, the static power consumption of the power device mainly working in the switching mode is continuously reduced, the static performance is greatly improved, and meanwhile, due to the increase of the switching frequency, the dynamic performance gradually becomes a main factor influencing the performance of the power device. Dynamic stability can affect, among other things, the level of Electromagnetic Interference (EMI) throughout the device application circuit. In addition, in the application of the device, it is desirable that the on-time and the off-time of the driving circuit control device are as short as possible to reduce the instantaneous power consumption of the device for on-and-off, and on the premise that the on-and-off transient state of the device can reach a certain stability index, the on-and-off time of the device is shortened as much as possible, and the on-and-off stability of the device also needs to be researched. Therefore, the dynamic stability performance of the power device is reliably evaluated, so that the power device is not only beneficial to guiding the practical application of the power device, but also beneficial to feeding back the design of the device, and the performance of the device is improved.
In practical application, the main source of EMI when the device is turned on and off is self-oscillation of the device caused by parasitic inductance, capacitance, and the like, and the parasitic parameters mainly come from the device itself, a packaging lead wire, a driving circuit, a peripheral circuit, and the like, so that the device, the driving circuit, other peripheral circuits, working conditions, and the like need to be selectively regarded as a system according to needs, and stability analysis is performed on the system to guide the design of a control algorithm. The existing stability analysis method mainly comprises the steps of establishing a transfer function of a system, finding out a characteristic equation, judging the stability of the system through a Route criterion, and simultaneously providing value ranges of parameters influencing the stability of the system. For device applications, a method capable of performing stability determination in real time is currently lacking. Therefore, it is necessary to develop a method for determining the stability of the power device in real time.
Disclosure of Invention
The invention aims to solve the technical problem in the prior art, and provides a method for evaluating the dynamic stability performance of a power device by combining a control theory and aiming at the switching transient process of the power device.
In order to solve the above technical problem, an embodiment of the present invention provides a method for evaluating dynamic stability of a power device, including the following steps:
the method comprises the steps that based on an equivalent circuit of a power device, sample data of the power device under different working conditions are obtained through simulation and experiments of the power device in a specific application circuit under different working conditions, the sample data are time-varying parameters and time-invariant parameters, and the sample data under each working condition correspond to a sample point;
establishing a state space equation of the power device according to the sample data in each sample point, thereby obtaining a system matrix;
substituting the system matrix into a Lyapunov equation to solve a matrix for judging stability;
judging whether the matrix is positive through Sylvester criterion, if so, stabilizing the power device of the sample point, classifying the sample point as a stable point, if not, stabilizing the power device of the sample point, and classifying the sample point as an unstable point;
through counting the number of the unstable points and the number of the stable points, the unstable degree index of the power device can be obtained, so that whether the power device is stable or not is judged, and the unstable degree is defined as the proportion of the number of the unstable points to the total number of the sample points in the whole process in the switching-on or switching-off transient process.
On the basis of the technical scheme, the invention can be further improved as follows.
Further, the equivalent circuit based on the power device is used for simulating and testing the power device in a specific application circuit under different working conditions to obtain sample data of the power device under different working conditions, and comprises the equivalent circuit based on the power device, and time-varying parameters and time-invariant parameters of the power device are obtained through parameter extraction experiments, model files provided by a device manufacturer and product data manuals provided by the device manufacturer or parameter soft measurement.
Further, establishing a state space equation of the power device according to the sample data in each sample point includes obtaining a transfer function of the power device by using kirchhoff's law according to the sample data, and obtaining the state space equation according to the transfer function.
Further, the power device is an Insulated Gate Bipolar Transistor (IGBT), a power Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET), a Thyristor (Thyristor), or a Gate turn-off Thyristor (GTO).
The invention has the beneficial effects that: the dynamic stability performance evaluation method of the power device can judge the dynamic stability performance of the power device according to the parameters of the power device in real-time operation, effectively evaluate the EMI level of the power device, is beneficial to guiding the practical application of the power device, and provides reference for the design optimization of the power device.
Drawings
FIG. 1 is an equivalent circuit diagram of a SiC-MOS power device;
FIG. 2 is a BUCK-type simulation test circuit for verifying a dynamic stability performance evaluation method of a power device according to an embodiment of the present invention;
fig. 3 is a diagram illustrating an on-waveform, an instability and an EMI level at a gate resistance of 10 Ω obtained by a method for evaluating dynamic stability of a power device according to an embodiment of the present invention;
fig. 4 is a diagram illustrating an off waveform, an instability and an EMI level at a gate resistance of 10 Ω obtained by a method for evaluating dynamic stability of a power device according to an embodiment of the present invention;
fig. 5 shows the turn-on waveform, the instability and the EMI level at a gate resistance of 20 Ω obtained by a method for evaluating the dynamic stability of a power device according to an embodiment of the present invention;
fig. 6 shows the turn-off waveform, the instability and the EMI level at a gate resistance of 20 Ω obtained by the method for evaluating the dynamic stability of a power device according to the embodiment of the present invention;
fig. 7 shows the turn-on waveform, the instability and the EMI level at a gate resistance of 30 Ω obtained by a method for evaluating the dynamic stability of a power device according to an embodiment of the present invention;
fig. 8 is a diagram illustrating an off waveform, an instability and an EMI level at a gate resistance of 30 Ω obtained by a method for evaluating dynamic stability of a power device according to an embodiment of the present invention;
FIG. 9 is a MAP graph of turn-on process instability versus EMI (intermediate in current harmonic amplitude);
FIG. 10 is a MAP graph of turn-off process instability versus EMI (with intermediate amounts of current harmonic amplitude);
fig. 11 is a diagram illustrating turn-on and turn-off waveforms and instability degrees of an IGBT load current of 26A obtained by a method for evaluating dynamic stability of a power device according to an embodiment of the present invention;
fig. 12 shows turn-on and turn-off waveforms and instability degrees of an IGBT load current of 40A obtained by a dynamic stability performance evaluation method of a power device according to an embodiment of the present invention;
FIG. 13 is a graph of power at two different load turn-on transients;
FIG. 14 is a power spectrum of two different load turn-on transients;
FIG. 15 is power for two different load turn-off transients;
fig. 16 is a power spectrum of two different load turn-off transients.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention.
The state space equation of a power device (such as SiC-MOS, Si-IGBT and the like) is actually characterized by a linear constant system, but the turn-on or turn-off process of the power device is a nonlinear time-varying system, because a system matrix has parameters which vary along with the turn-on and turn-off processes of the device, taking SiC-MOS as an example, the state space equation system matrix comprises a gate-drain capacitor CgdGate source capacitance CgsAnd an on-resistance RonIsochronously variable parameters, i.e. at openingOr off, is applicable. In order to correctly describe the nonlinearity and time-varying property of the on-off process of the power device, the invention adopts a statistical method for processing, namely sampling on or off, each sample data uses the state space equation and the Lyapunov stability criterion to judge the stability of the device in the state of the current sampling point, when the number of the sampling points reaches enough, namely the samples are big enough, the stable point and unstable distribution of the device can be reflected when the device is switched on or switched off, so that the stable degree and the variation trend of the switching on or off of the device can be reflected macroscopically according to the proportion of the two points, and finally, reference is provided for stability control. Therefore, the state space equation of the power device is established in the form of a linear steady system, the stability degree of the power device is judged by means of a statistical method, compared with the method of directly establishing the state space equation of a nonlinear time-varying system and judging the stability by using a Lyapunov method for judging the nonlinear time-varying system, the method has the advantages that the complexity is greatly reduced, the calculated amount is greatly reduced, the possibility of real-time calculation is realized, and the model and the method can be used for actual real-time stability control on the premise of balancing calculation resource overhead.
A method for evaluating dynamic stability of a power device according to a first embodiment of the present invention includes the following steps:
the method comprises the steps that based on an equivalent circuit of a power device, sample data of the power device under different working conditions are obtained through simulation and experiments of the power device in a specific application circuit under different working conditions, the sample data are time-varying parameters and time-invariant parameters, and the sample data under each working condition correspond to a sample point;
establishing a state space equation of the power device according to the sample data in each sample point, thereby obtaining a system matrix;
substituting the system matrix into a Lyapunov equation to solve a matrix for judging stability;
judging whether the matrix is positive through Sylvester criterion, if so, stabilizing the power device of the sample point, classifying the sample point as a stable point, if not, stabilizing the power device of the sample point, and classifying the sample point as an unstable point;
through counting the number of the unstable points and the number of the stable points, the unstable degree index of the power device can be obtained, so that whether the power device is stable or not is judged, and the unstable degree is defined as the proportion of the number of the unstable points to the total number of the sample points in the whole process in the switching-on or switching-off transient process.
In the above embodiment, the time-varying parameter mainly includes Cgd、Cds(in MOSFET) or Cgc、Cce(in IGBT), RonAnd the like.
Optionally, the equivalent circuit based on the power device performs simulation and experiment on the power device in a specific application circuit under different working conditions to obtain sample data of the power device under different working conditions, and includes the equivalent circuit based on the power device, and device physical parameters of the power device are obtained by performing parameter extraction experiment, model files provided by a device manufacturer, and product data manuals provided by the device manufacturer or performing soft parameter measurement, and are time-varying parameters and time-invariant parameters.
In the above embodiment, taking SiC-MOS as an example, the capacitor CgdAnd CdsIs two variable capacitors, and is dependent on drain-source voltage VDSCan be respectively fitted with the capacitance curve diagrams of the product data manualDSThe formula (2). On-resistance RonIt is possible to pass the real-time test VDSAnd IDSAnd obtained by ohm's law.
Optionally, the establishing a state space equation of the power device according to the sample data in each sample point includes obtaining a transfer function of the power device according to the sample data by using kirchhoff's law, and obtaining the state space equation according to the transfer function.
In the above embodiment, the state space equation may also be directly established according to the sample data in each sample point.
Optionally, the power device is an Insulated Gate Bipolar Transistor (IGBT), a power Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET), a Thyristor (Thyristor), or a Gate turn-off Thyristor (GTO).
A first embodiment of the present invention will be described in detail below with respect to a specific power device object of SiC-MOS, and FIG. 1 shows an equivalent circuit of a SiC-MOS system, wherein R isGIs an internal gate resistance and a package line parasitic resistance, LGFor packaging line parasitic inductance, RSIs a source electrode packaging line parasitic resistance, LSFor source packaging line parasitic inductance, RDIs parasitic resistance of drain electrode packaging circuit, LDParasitic inductance of drain packaging lines. For the power device itself, as shown in FIG. 1, it is equivalent to three capacitors Cgs、Cgd、CdsOn-resistance RonControllable current source gmVGSIn which C isds、RonAnd a controllable current source in parallel relation. The dashed line in fig. 1 represents the inside of the device, including three ways of package, module, or die, and the obtained state space equation corresponds to a specific way, and depends on the value of the parameter in the state space equation, that is, the relevant parameter of the package module is considered, or only the relevant parameter of the die is considered.
The transfer function of the power device can be obtained by using kirchhoff law:
Figure BDA0002844500930000061
wherein
LL＝LDLG+LDLS+LGLS
RR＝RDRG+RDRS+RGRS
CC＝CdsCgd+CdsCgs+CgdCgs
LR＝LDRG+LGRD+LDRS+LSRD+LGRS+LSRG
Converting the transfer function of the power device into a state space equation:
Figure BDA0002844500930000071
Figure BDA0002844500930000072
Figure BDA0002844500930000073
Figure BDA0002844500930000074
where x is the state vector, y is the output vector, u is the control vector, A is the system matrix, B is the input matrix, and C is the output matrix. The state space equation of other types of power devices can be obtained by the method.
After the system matrix A is obtained, the system matrix A is substituted into a Lyapunov equation: a. theTAnd (3) obtaining a matrix P for judging stability, wherein I is an identity matrix, judging whether P is positive according to a Sylvester criterion, if so, indicating that the power device is stable currently, and if not, indicating that the power device is unstable currently.
The acquisition of the physical parameters of the device is the first step of judging whether the system matrix A is stable, the parameters in A are divided into two types,
i.e. parameters that do not change with changes in external conditions and parameters that change with changes in external conditions (e.g. time), i.e. constant parameters and time-varying parameters. The former includes all inductance parameters, resistance parameters and CgsThe latter comprising Cgd、Cds、Ron. These parameters can be obtained using parameter extraction experiments or fitting according to a model file or product data manual provided by the manufacturer or soft measurements of the parameters. For example, when fitting acquisition is performed according to a product data manual provided by a manufacturer, CgdAnd CdsThe two variable capacitors are changed along with the change of the drain-source voltage and can respectively correspond to a reverse capacitance curve graph and an output capacitance curve graph in a product data manual, and formulas of the variable capacitors and the output capacitance curve graphs related to the drain-source voltage can be respectively fitted through the capacitance curve graphs of the product data manual. RonThe real-time calculation is carried out by the formula to obtain: ron＝VDS/IDS。
The stability evaluation method based on the Lyapunov stability criterion and mathematical statistics is used for performing simulation verification on the SiC-MOS and experimental verification on the IGBT respectively.
And developing a corresponding algorithm for simulation and experimental verification by using a Matlab tool according to a state space equation of the SiC-MOS equivalent circuit and the dynamic stability performance evaluation method of the power device. A SPICE model file of the existing SiC-MOS is selected, and a BUCK circuit is built on an LTspice simulation platform, as shown in figure 4. For time-varying parameters, C can be fitted according to the product data manual of the SiC-MOSgdAnd CdsCurve line. For the on-resistance RonAccording to V collected by each sampleDSAnd IDSAnd (6) performing calculation. And during verification, different external gate resistors are respectively taken to judge the instability degree and the EMI level of switching on and switching off. The EMI level is measured in di/dt by subjecting the sample to Fast Fourier Transform (FFT) and observing the relationship between the amplitude, frequency and instability of its harmonic components. The results of the stability evaluation of the SiC-MOS switch transient in the simulation circuit are shown in fig. 5 to 10, where Unstable level, i.e., instability, represents that the determination result is Unstable and stable as "0" and "1", respectively, and the heights of "0" and "1" represent the number of sample points in a certain time period. Summarizing the graphs 3-8 according to the turn-on and turn-off respectively, adding three groups of simulation, obtaining instability data and corresponding current harmonic amplitude and current main harmonic frequencyAccordingly, they are drawn together in the form of contour MAPs (MAP MAPs), as shown in fig. 9-10, which plot the data for each instability point; as the color deepens, the instability degree increases, and the corresponding current harmonic amplitude also increases; and the larger the current harmonic amplitude, the higher the EMI level, so a linear relationship between the instability and the EMI level is illustrated. Simulation results prove that the stability evaluation method based on the Lyapunov stability criterion and mathematical statistics is suitable for SiC-MOS.
The following experimental verification is carried out by taking the Si-IGBT as a power device object in combination with the attached drawings: different load currents are applied to the Si-IGBT on the existing dynamic test platform of the power device to obtain the on and off waveforms of the Si-IGBT. The time-invariant parameters in the state space equation system matrix A can be obtained through the model file of the Si-IGBT. For time-varying parameters, CgcAnd CceFitting can be performed by the capacitance curve diagram in the product data manual, the resistance RonObtained by fitting through an I-V characteristic curve in a product data manual. During verification, two different load currents, 26A and 40A respectively, are set, and instability and variation trend of EMI level during switching on and switching off are respectively judged. The EMI level is measured by the instantaneous power of the switching-on and switching-off processes, namely, the instantaneous power of each sample is subjected to Fast Fourier Transform (FFT) to obtain a spectrogram to observe harmonic components of the spectrogram. As shown in fig. 11 and 12, the result of the experimental verification is that Unstable level in the graph is Unstable, where a sample point of "0" represents that the sample point is determined as an Unstable point after passing through the stability, and a sample point of "1" represents that the sample point is determined as a stable point after passing through the stability. It can be seen that the instability of the turn-on and turn-off process is greater at a load current of 40A than at a load current of 26A. Fig. 13 to 16 are frequency spectra obtained by Fast Fourier Transform (FFT) of instantaneous power and instantaneous power at on and off, respectively, where the abscissa is normalized frequency, and the harmonic amplitude at 26A current load is smaller than that at 40A current load, i.e., the EMI level at 26A current load is smaller than that at 40A current load. Experimental results prove that the stability evaluation method based on Lyapunov stability criterion and mathematical statistics provided by the invention is suitable for SAnd i-IGBT. The experimental result also shows that the instability of the power device system obtained by the method provided by the invention has positive correlation with the instability and EMI level of the power device in the actual switching transient process. Therefore, the instability index can be used as a key index for evaluating the dynamic stability performance of the power device, and the EMI level of the device can be effectively evaluated.
The method is based on the equivalent circuit of the power device, sample data of the power device under different working conditions is obtained, a state space equation of the power device is established according to the sample data, a system matrix is obtained, and the system matrix is substituted into a Lyapunov equation to solve a matrix for judging stability. The invention can obtain the related parameters of the power device changing along with the time through the parameter extraction experiment or according to the model file provided by the manufacturer or the product data manual provided by the manufacturer or according to the soft measurement of the parameters, and further can dynamically determine the matrix; whether the matrix is positive is judged through Sylvester criterion, whether the power device is stable under different working conditions is obtained, and the instability index of the power device is obtained through counting the number of instability points and stable points, so that whether the power device is stable is judged. The dynamic stability performance of the power device can be judged according to the parameters of the power device in real-time operation, the EMI risk level of the power device is effectively evaluated, the practical application of the power device is favorably guided, reference is provided for the design optimization of the power device, and the scheme has the advantages of simplicity, high efficiency, transportability and the like.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (4)

1. A method for evaluating dynamic stability performance of a power device is characterized by comprising the following steps:
the method comprises the steps that based on an equivalent circuit of a power device, sample data of the power device under different working conditions are obtained through simulation and experiments of the power device in a specific application circuit under different working conditions, the sample data are time-varying parameters and time-invariant parameters, and the sample data under each working condition correspond to a sample point;
establishing a state space equation of the power device according to the sample data in each sample point, thereby obtaining a system matrix;
substituting the system matrix into a Lyapunov equation to solve a matrix for judging stability;
judging whether the matrix is positive through Sylvester criterion, if so, stabilizing the power device of the sample point, classifying the sample point as a stable point, if not, stabilizing the power device of the sample point, and classifying the sample point as an unstable point;
through counting the number of the unstable points and the number of the stable points, the unstable degree index of the power device can be obtained, so that whether the power device is stable or not is judged, and the unstable degree is defined as the proportion of the number of the unstable points to the total number of the sample points in the whole process in the switching-on or switching-off transient process.
2. The method according to claim 1, wherein the equivalent circuit based on the power device performs simulation and experiment on the power device in a specific application circuit under different working conditions to obtain sample data of the power device under different working conditions, and comprises the step of obtaining time-varying parameters and time-invariant parameters of the power device through parameter extraction experiment, model files provided by a device manufacturer, and a product data manual provided by the device manufacturer or soft parameter measurement based on the equivalent circuit based on the power device.
3. The method according to claim 1, wherein the establishing a state space equation of the power device according to the sample data in each sample point comprises obtaining the transfer function of the power device according to the sample data by kirchhoff's law, and obtaining the state space equation according to the transfer function.
4. The method of claim 1, wherein the power device is an Insulated Gate Bipolar Transistor (IGBT), a power-Oxide-Semiconductor Field-Effect Transistor (MOSFET), a Thyristor (Thyristor), or a Gate turn-off Thyristor (GTO).
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张金平: ""IGBT新技术及发展趋势"", 《大功率变流技术》 *
曾潇: ""IGBT并联电流均衡模型和神经网络控制研究"", 《中国优秀博硕士学位论文全文数据库（博士） 信息科技辑》 *

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Application publication date: 20210427