CN116819176B - An impedance spectrum generation method based on argument transformation - Google Patents
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Abstract
The invention discloses an impedance spectrum generation method based on amplitude-angle transformation, which belongs to the technical field of measuring electric variables and is used for generating an impedance spectrum on the premise of not using an impedance meter, and comprises the steps of constructing a test circuit, calculating the sum of the impedance of a protection resistor and the impedance of an object to be measured and obtaining a further calculation formula of the sum; calculating four phases, and taking the values of the four phases to further calculate a formula; and separating the resistance and reactance in the sum of the impedance of the protection resistor and the impedance of the object to be detected, calculating the impedance spectrum and the phase spectrum of the object to be detected, and finally respectively performing fast Fourier transform on the input signal and the output signal to calculate the phase of the input signal. According to the invention, the cost of the instrument is greatly reduced, and the measured data show that the extreme point measuring position of the measured impedance amplitude spectrum is completely consistent with the simulation, the zero crossing point of the phase spectrum is completely consistent with the position in the simulation result, the cable impedance amplitude spectrum is continuously attenuated along with the increase of the frequency, and the cable impedance amplitude spectrum is completely consistent with the simulation result, so that the noise resistance of the invention is very excellent.
Description
Technical Field
The invention discloses an impedance spectrum generation method based on amplitude-angle transformation, and belongs to the technical field of measuring electric variables.
Background
Impedance spectroscopy is a graph representing the impedance characteristics of a circuit, material or system at different frequencies, which describes the response of an element in an ac circuit to current and voltage. Impedance spectra are generally plotted with frequency on the horizontal axis and impedance values (including resistance and reactance) on the vertical axis, and exhibit characteristics of elements such as capacitance, inductance, and resistance. In the fields of circuit analysis and electronic engineering, impedance spectroscopy has wide applications: in radio frequency designs, impedance spectroscopy can be used to optimize antenna matching and power transfer efficiency; in the biomedical field, impedance spectroscopy is used to measure the electrical resistance and conductivity of biological tissue, thereby providing information about tissue structure and function. The impedance spectrum is usually drawn by experimental measurement data or calculation through a mathematical model, and the current experiment is mainly performed by using an impedance analyzer, but the impedance analyzer has high equipment price, complex operation and possible influence of external environment and power supply noise on the measurement result.
Disclosure of Invention
The invention aims to provide an impedance spectrum generation method based on amplitude-angle transformation, which aims to solve the problem of high cost of drawing impedance spectrum by measuring through an impedance meter in the prior art.
An impedance spectrum generation method based on amplitude-angle transformation comprises the following steps:
s1: constructing a test circuit;
s2: calculating the sum of the protection resistance and the impedance of the object to be measured；
S3: obtainingIs a further calculation formula of (2);
s4: calculating four phases;
s5: bringing the values of four phases intoFurther calculation of (2)And use +.>And->Replacement->And->；
S6: separationResistance of->And reactance->；
S7: calculating an object to be measuredImpedance spectrum +.>And phase spectrum->；
S8: performing fast fourier transform on the input signal and the output signal respectively;
s9: calculating the phase of an input signal。
S1 comprises the following steps:
the first grounding point GND1 is connected with a signal source, the signal source generates alternating current signals, and the signal sources are sequentially connected in series: series resistorProtection resistor->Object to be measured->，/>The negative electrode of the operational amplifier is connected, and the output end of the operational amplifier is connected in series with a first resistor，/>The first acquisition card is connected in series, and a feedback resistor is arranged at the right side of the first acquisition card>Parallel to the operational amplifier, a feedback capacitor>And->Parallel connection;
and->A second acquisition card is arranged between the two, and the positive electrode of the operational amplifier is sequentially connected with a second resistor +.>And a second ground GND2.
S2 comprises the following steps:
let the amplitude of the output signal of the signal source beFlow through->Is +.>Let->，/>Is the sum of the protection resistance and the impedance of the object to be measured, < + >>For the resistance of the object to be measured, the drug is->The method comprises the following steps:
。
s3 comprises the following steps:
make the operational amplifier output asThe feedback network is +.>，/>The method comprises the following steps:
；
in the method, in the process of the invention,j represents the imaginary part, < >>，/>For periods of->To obtain the frequency of the signal during testIs calculated according to the following formula:
，/>；
e is a constant value, and is a constant value,changing the sign of the signal of the operational amplifier.
S4 comprises the following steps:
the following phases are calculated:
；
for the phase of the input signal>For the phase of the output signal>For feeding back part phase +>To protect the resistor andis a phase of (a) of (b).
S5 comprises the following steps:
bringing into the equation for calculating the phase four timesIs calculated according to the following formula:
；
；
；
let the effective value of the input signal beThe effective value of the output signal is +.>Use +.>And->Replacement->And->：
。
S6 comprises the following steps:
separationResistance of->And reactance->：
；
。
S7 comprises the following steps:
object to be measuredBy resistance->And reactance->Composition, i.e.)>：
；
；
Obtaining the object to be measuredImpedance spectrum +.>And phase spectrum->。
S8 comprises the following steps:
calculating effective value of input signal and output signal，/>And the phase of the object to be measured->The input and output signals are respectively subjected to fast Fourier transform, and the frequency of the test signal is +.>The step frequency is set to +.>Let the step frequency be 10->Select sampling points +.>Is->Dot, frequency resolution->；
Is provided withThe number of points is->The sampling frequency of the acquisition card is->FFT is fast Fourier transform, and the signal frequency is +.>：
；
For the +.>Dots, set up->The dot result is +.>Effective value of input signal +.>The method comprises the following steps:
。
s9 comprises the following steps:
is provided withThe real part of (2) is->The imaginary part is->Phase of input signal->The method comprises the following steps:
。
compared with the prior art, the invention has the following beneficial effects: according to the invention, the cost of the instrument is greatly reduced, and the measured data show that the extreme point measuring position of the measured impedance amplitude spectrum is completely consistent with the simulation, the zero crossing point of the phase spectrum is completely consistent with the position in the simulation result, the cable impedance amplitude spectrum is continuously attenuated along with the increase of the frequency, and the cable impedance amplitude spectrum is completely consistent with the simulation result, so that the noise resistance of the invention is very excellent.
Drawings
FIG. 1 is a technical flow chart of the present invention;
FIG. 2 is a circuit diagram of a distributed parameter equivalent to a transmission line;
fig. 3 is a graph of 200 m open cable impedance magnitude.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions in the present invention will be clearly and completely described below, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
An impedance spectrum generation method based on amplitude-angle transformation comprises the following steps:
s1: constructing a test circuit;
s2: calculating the sum of the protection resistance and the impedance of the object to be measured；
S3: obtainingIs a further calculation formula of (2);
s4: calculating four phases;
s5: bringing the values of four phases intoIs used, and +.>And->Replacement->And->；
S6: separationResistance of->And reactance->；
S7: calculating an object to be measuredImpedance spectrum +.>And phase spectrum->；
S8: performing fast fourier transform on the input signal and the output signal respectively;
s9: calculating the phase of an input signal。
S1 comprises the following steps:
the first grounding point GND1 is connected with a signal source, the signal source generates alternating current signals, and the signal sources are sequentially connected in series: series resistorProtection resistor->Object to be measured->，/>The negative electrode of the operational amplifier is connected, and the output end of the operational amplifier is connected in series with a first resistor，/>The first acquisition card is connected in series, and a feedback resistor is arranged at the right side of the first acquisition card>Parallel to the operational amplifier, a feedback capacitor>And->Parallel connection;
and->A second acquisition card is arranged between the two, and the positive electrode of the operational amplifier is sequentially connected with a second resistor +.>And a second ground GND2.
S2 comprises the following steps:
let the amplitude of the output signal of the signal source beFlow through->Is +.>Let->，/>Is the sum of the protection resistance and the impedance of the object to be measured, < + >>For the resistance of the object to be measured, the drug is->The method comprises the following steps:
。
s3 comprises the following steps:
make the operational amplifier output asThe feedback network is +.>，/>The method comprises the following steps:
；
in the method, in the process of the invention,j represents the imaginary part, < >>，/>For periods of->To obtain the frequency of the signal during testIs calculated according to the following formula:
，/>；
e is a constant value, and is a constant value,changing the sign of the signal of the operational amplifier.
S4 comprises the following steps:
the following phases are calculated:
；
for the phase of the input signal>For the phase of the output signal>For feeding back part phase +>To protect the resistor andis a phase of (a) of (b).
S5 comprises the following steps:
bringing into the equation for calculating the phase four timesIs calculated according to the following formula:
；
；
；
let the effective value of the input signal beThe effective value of the output signal is +.>Use +.>And->Replacement->And->：
。
S6 comprises the following steps:
separationResistance of->And reactance->：
；
。
S7 comprises the following steps:
object to be measuredBy resistance->And reactance->Composition, i.e.)>：
；
；
Obtaining the object to be measuredImpedance spectrum +.>And phase spectrum->。
S8 comprises the following steps:
calculating effective value of input signal and output signal，/>And the phase of the object to be measured->The input and output signals are respectively subjected to fast Fourier transform, and the frequency of the test signal is +.>The step frequency is set to +.>Let the step frequency be 10->Select sampling points +.>Is->Dot, frequency resolution->；
Is provided withThe number of points is->The sampling frequency of the acquisition card is->FFT is fast Fourier transform, and the signal frequency is +.>：
；
For the +.>Dots, set up->The dot result is +.>Effective value of input signal +.>The method comprises the following steps:
。
s9 comprises the following steps:
is provided withThe real part of (2) is->The imaginary part is->Phase of input signal->The method comprises the following steps:
。
the invention uses the technical route of amplitude-angle transformation to generate the test frequency inImpedance spectrum in the range. The method is mainly applied to how to rapidly acquire and research the impedance spectrum of the object to be detected. The acquisition flow of the signals in the research scheme is shown in figure 1, the signals are generated by a signal generator, and then are formed after filtering, amplifying and amplifying, the amplitude is programmable, and the frequency is +.>。/>To protect the resistor, prevent->Too small results in too large a magnification resulting in circuit failure. And the feedback capacitor prevents self-oscillation of the operational amplifier. Even when operating at high frequencies +.>Can not be fixed as->Ohm, because the signal cable of the acquisition card has an input capacitance when the acquisition card is connected, signal attenuation is easy to cause, thus +.>It needs to be tuned to the optimal value. According to the circuit diagram, an input signal and an output signal are obtained, so that +.>Is used, and the impedance angle.
The fast Fourier transform stepping is utilized to remove the noise influence to the maximum extent, so the effective value and the phase of the signal are calculated by utilizing the fast Fourier transform scheme. By means ofThe stepping can remove noise influence to the maximum extent, and the phase difference calculation is very accurate.
The availability and the testing accuracy of the method are verified by using the impedance spectrum of the test cable, a 10kV XLPE power cable with the length of 100m is tested in a laboratory environment, and the test result is compared with the simulation modeling result. The cable can be equivalently analyzed by using a distribution parameter model under the condition of high frequency or longer cable length, and the equivalent distribution parameter circuit of the transmission line is shown as figure 2, wherein G, R, L, C and G respectively represent the resistance, inductance, capacitance and conductance of the unit length of the transmission line by taking the position of a power supply as the origin of coordinates, and then the voltage phasor at the position x of the transmission line is V (x) and the current phasor is I (x)
The voltage vector and the current vector after passing through the cable of unit length are as follows:
V（x）+dV，I（x）+dI；
order theAs the reflection coefficient at the load side, if the load is open, the reflection coefficient is real +.>The propagation coefficients of the transmission line are:
；
resistance per unit length +.>Is a single sheetInductance of bit length->Is the conductance of the potential length, ">Capacitance per unit length. />Alpha is the decay constant and beta is the phase constant. In addition, β can be expressed as +.>Wherein: v is the wave velocity of the electromagnetic wave in the cable and f is the frequency.
；
Wherein the method comprises the steps ofFor the propagation coefficient of the transmission line, < >>Is the characteristic impedance of the transmission line. The total length of the cable is +.>At the frequency +.>Lower, at any position from the head end of the cable +.>Input impedance spectrum ∈>Expressed as:
；
in FIG. 3, 200 m open circuit cable impedance amplitude spectrum, characteristic impedance is constructed72.25 ohm, the wave speed of the electromagnetic wave is +.>Meter/second. The measured results are shown in the graph. The impedance spectrum has three characteristics of periodicity, attenuation and signal variability.
(1) The periodicity refers to the maxima and minima of the cable impedance amplitude and the phase spectrum periodicity, the maxima of the head impedance amplitude occur at equally-spaced frequency points, and the spaced frequency isWhile the impedance phase spectrum exhibits periodic zero crossings at these frequency points.
(2) Attenuation refers to the characteristic that the maximum values of the cable impedance amplitude and phase spectrum are attenuated as the frequency increases. The cable impedance amplitude spectrum in the actual measurement result graph is continuously attenuated along with the increase of frequency.
(3) The rapid change means that the impedance changes very rapidly near the maximum value of the impedance amplitude spectrum and near the zero crossing point of the impedance phase spectrum, and the cable impedance amplitude spectrum in the actually measured result graph changes very rapidly near the maximum value and the minimum value.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6502046B1 (en) * | 1999-03-13 | 2002-12-31 | Korea Kumbo Petrochemical Co. Ltd | Laplace transform impedance spectrometer and its measurement method |
| CN109726452A (en) * | 2018-12-12 | 2019-05-07 | 浙江大学 | An online proton exchange membrane fuel cell fault diagnosis method based on impedance spectroscopy |
| CN111580006A (en) * | 2020-05-29 | 2020-08-25 | 中国电力科学研究院有限公司 | Online measurement method and system for dynamic impedance of battery |
| WO2022062651A1 (en) * | 2020-09-27 | 2022-03-31 | 比亚迪股份有限公司 | Method for generating electrochemical impedance spectroscopy of battery, medium, and computer device |
| CN116346219A (en) * | 2023-03-24 | 2023-06-27 | 国网山东省电力公司聊城供电公司 | Optical fiber fault test system resistant to optical interference |
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6502046B1 (en) * | 1999-03-13 | 2002-12-31 | Korea Kumbo Petrochemical Co. Ltd | Laplace transform impedance spectrometer and its measurement method |
| CN109726452A (en) * | 2018-12-12 | 2019-05-07 | 浙江大学 | An online proton exchange membrane fuel cell fault diagnosis method based on impedance spectroscopy |
| CN111580006A (en) * | 2020-05-29 | 2020-08-25 | 中国电力科学研究院有限公司 | Online measurement method and system for dynamic impedance of battery |
| WO2022062651A1 (en) * | 2020-09-27 | 2022-03-31 | 比亚迪股份有限公司 | Method for generating electrochemical impedance spectroscopy of battery, medium, and computer device |
| CN116346219A (en) * | 2023-03-24 | 2023-06-27 | 国网山东省电力公司聊城供电公司 | Optical fiber fault test system resistant to optical interference |
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