A method for measuring and calibrating impedance based on IQ demodulation

Abstract

The application discloses a kind of based on IQ demodulation calculation impedance measurement and calibration method, belong to the technical field of measurement calibration of impedance.The application is measured to the voltage and current of coupling voltage wave signal and current wave signal in voltage current coupler circuit with coupling voltage wave signal and current wave signal, obtains original current signal and original voltage signal, obtains the impedance value in circuit, as known impedance;According to known impedance and original current signal, original voltage signal, according to the direct current signal I value and direct current signal Q value corresponding to the known impedance reflected by voltage wave and current wave, and then calculate the error M caused by the final calculation impedance, the final standard impedance value is calculated by correcting the error brought by reading value;Test impedance is input into known impedance with radio frequency power, test impedance is input into known impedance with radio frequency power, introduce calibration factor can confirm that actual impedance and test impedance exist following relationship, determine actual impedance.

Description

Technical Field

[0001] This invention belongs to the field of impedance measurement and calibration technology, and in particular relates to a method for measuring and calibrating impedance based on IQ demodulation calculation. Background Technology

[0002] Impedance calculations often rely on coupled current and voltage signals. In practical applications, coupled signals often produce amplitude and phase errors. To address these errors in the circuit system itself, a more precise calculation and calibration method is often required. Traditional calibration methods often require collecting multiple impedance values ​​for high-precision calibration. Summary of the Invention

[0003] The purpose of this invention is to provide a method for measuring and calibrating impedance based on IQ demodulation calculation.

[0004] This invention is achieved through the following technical solution:

[0005] This invention discloses a method for measuring and calibrating impedance based on IQ demodulation. It measures the voltage and current of the coupled voltage and current signals in a voltage-current coupler circuit to obtain the original current signal. and the original voltage signal ;

[0006] The impedance value in the circuit is obtained through standard components or measurement methods and is used as the known impedance.

[0007] Based on the known impedance and the original current signal Original voltage signal This yields two sets of DC signal I and DC signal Q values ​​that reflect voltage and current waves, respectively.

[0008] Based on the DC signal I and DC signal Q values ​​that reflect voltage and current waves and the corresponding known impedance, the error M that affects the final calculated impedance is calculated, and the error M brought by the impedance detection system of IQ demodulation calculated impedance is set as the standard calibration factor of a single system.

[0009] Read the numerical value with errors, and calculate the final standard impedance value by correcting the errors caused by the reading value;

[0010] Also includes test impedance Test impedance The result is obtained by dividing the voltage wave and current wave with amplitude and phase shifts that are coupled out through the coupling circuit when radio frequency power is applied to a known impedance.

[0011] Introducing calibration factors It can be confirmed and The following relationship exists to determine the actual impedance. :

[0012]

[0013]

[0014] Where M is the calibration factor, and... This indicates the amplitude error of the voltage output signal. This indicates the phase shift of the voltage output signal. This indicates the amplitude error of the current output signal. This indicates the phase shift of the current output signal.

[0015] Among them, the corresponding DC signal Values ​​and DC signals Value through the original voltage signal Original current signal It can be obtained by mixing with a signal of the same frequency and then passing it through a low-pass filter;

[0016] Specifically: DC signal With DC signal Component calculation and representation of the original signal:

[0017]

[0018]

[0019] Specifically, DC signals I and Q can represent the original signals that have undergone amplitude and phase shifts after being coupled by the circuit, satisfying the following relationship:

[0020]

[0021]

[0022] in: This represents the true amplitude of the original signal. Represents the true phase of the original signal. I(t) represents the signal obtained after filtering out high-frequency signal components through a low-pass filter. The signal before passing through the LPF is related to time t. After passing through the LPF, the high-frequency components are filtered out, so the signal after passing through the LPF is independent of time t, and only the DC component remains. To describe a single specific signal, two dimensions, amplitude and phase, are required. After converting the signal into the complex domain, its two dimensions can also be described.

[0023] This represents the error in amplitude change caused by the voltage passing through a fixed circuit system. This refers to the fixed phase shift of the system caused by the sampled voltage or current signal passing through a fixed circuit system. This represents the total gain produced by the entire circuit, that is, the normalized gain of the circuit amplitude. This represents a complex number, where j represents the imaginary unit. This represents the addition of a real number of I and an imaginary number of Q.

[0024] Specifically, DC signal Obtaining:

[0025] The original coupled voltage signal is:

[0026] ;

[0027] After passing through the circuit system, both the phase and amplitude will be incorrect. After passing through the coupler that couples the voltage wave signal and the current wave signal, both the amplitude and phase of the original signal will change. This can be expressed as the signal after the change:

[0028] ;

[0029] local oscillator signal Multiplying them together gives:

[0030]

[0031] in, Indicates the original Abbreviation;

[0032] We can obtain the product-to-sum formula for trigonometric functions:

[0033]

[0034] High-frequency components are filtered out by a low-pass filter and then... The DC signal can be obtained after representing the total gain. .

[0035] Specifically, DC signal Obtaining:

[0036] For the local oscillator signal Multiplying them together gives:

[0037]

[0038] We can obtain the product-to-sum formula for trigonometric functions:

[0039]

[0040] Then, high-frequency components are filtered out by a low-pass filter and... The DC signal can be obtained after representing the total gain. .

[0041] Specifically, the original voltage signal and the original current signal There exists a real number field; it can be transformed to the complex number field.

[0042]

[0043] ;

[0044] A signal in the complex domain can be converted back to a signal in the real domain by taking its real part.

[0045]

[0046]

[0047] Original voltage signal The generated amplitude and phase offset signals and the original current signal The generated amplitude and phase offset signals We can obtain:

[0048]

[0049]

[0050] For actual impedance yes:

[0051]

[0052] The test impedance can be obtained through testing. It is:

[0053]

[0054] This represents the DC component I read from the voltage-coupled signal after IQ demodulation and then passing through an ideal filter. This represents the DC component Q of the voltage-coupled signal, after IQ demodulation and passing through an ideal filter. This represents the DC component I read from the current-coupled signal after IQ demodulation and then passing through an ideal filter. This represents the DC component Q of the current-coupled signal, after IQ demodulation and passing through an ideal filter. This value is then read during calibration, along with the inherent calibration factor coefficient within the system. Calculate the final true impedance.

[0055] It also includes impedance calibration: calculating the sum of the values ​​obtained by complex number operations after IQ demodulation following the connection of a known calibration impedance. and Satisfy the following formula:

[0056]

[0057]

[0058] , , , The corresponding mapped measured voltage and current waveforms represent two sets of IQ values ​​obtained after IQ demodulation following connection to a known calibration impedance, and these values ​​include errors. This indicates the amplitude error of the voltage output signal. This represents the amplitude error of the current output signal, while and This is the amplitude reading corresponding to the actual impedance value, and its ratio is any impedance. The ratio of is applied to any measured impedance including error.

[0059]

[0060] Then the system error factor:

[0061]

[0062] Therefore, the calibration factor can be derived from the data:

[0063]

[0064] Therefore, when faced with unknown impedance, one can read... , , , Calculate , This represents the value read from the voltage-coupled signal after IQ demodulation. This represents the value read from the voltage-coupled signal after IQ demodulation. This represents the value read from the current-coupled signal after IQ demodulation. This represents the value read from the current-coupled signal after IQ demodulation, and the corresponding value can be calculated. and Satisfy the following formula:

[0065]

[0066]

[0067] Simultaneously calculate their ratio:

[0068]

[0069] The final impedance then satisfies the formula:

[0070]

[0071] This is the error factor introduced through data derivation mentioned above. By calibrating with any impedance, the corresponding error factor is determined, and the corresponding true impedance is calculated based on the error factor reading.

[0072] The present invention has the following beneficial effects:

[0073] In voltage-current coupler circuits, voltage and current signals generate coupling errors. This invention designs a system that, while establishing the correspondence between voltage and current signals and two sets of IQ DC level signals, only requires passing a precise impedance and using formulas to calculate the precise impedance and the corresponding two sets of IQ DC levels. This yields the system's inherent error, allowing for the establishment of a stable linear relationship between the two sets of IQ DC levels and the voltage and current signals in the voltage-current coupler in subsequent calculations. The system is simple in structure, possesses elegant mathematical principles, and offers precise calculations.

[0074] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0075] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0076] Figure 1 This is a system block diagram for signal measurement and calibration. Detailed Implementation

[0077] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0078] like Figure 1 As shown, in the voltage-current coupler circuit, after the power source is connected to the load, the voltage signal is coupled out through the voltage and current detection probe and then coupled through the voltage-current coupling circuit to obtain the original voltage signal. With the original current signal Original voltage signal Original current signal By mixing with a signal of the same frequency and then passing it through a low-pass filter, the corresponding DC signal can be obtained. and DC signals The measured impedance value is then calculated. However, in actual calculations, phase and amplitude errors may occur in the signal. To address the error factor of the impedance detection system used for IQ demodulation impedance calculation, a known impedance needs to be input. The error factor is then calibrated in reverse using the IQ readings. Finally, given the voltage and current values ​​coupled from the unknown impedance, the error factor can be substituted into the calculation to arrive at the true impedance.

[0079] Specifically, a known impedance can be obtained through the impedance value of a standard component or by measurement methods. After measuring any known impedance, two sets of DC signals I and Q, reflecting voltage and current waves, are obtained. Based on these values ​​and the corresponding known impedance, the error M affecting the final calculated impedance can be calculated. The error M brought by the impedance detection system of IQ demodulation impedance calculation is set as the standard calibration factor of a single system. Then, by reading the erroneous values ​​and correcting the error brought by the reading values, the final standard impedance value can be read or calculated. When reading the I and Q values ​​reflecting the coupled voltage and current, the error can be set as the impedance calibration factor in the formula when using the impedance calculation method. Substituting the calibration factor coefficient M, the true impedance can be calculated.

[0080] A method for measuring and calibrating impedance based on IQ demodulation:

[0081] With the original coupled voltage signal For example:

[0082]

[0083] in This represents the true amplitude of the original signal. This represents the true phase of the original signal; however, after passing through the circuit system, both its phase and amplitude will be incorrect. After passing through the voltage and current detection probes that couple the voltage wave signal and the current wave signal, both the original signal amplitude and phase will change.

[0084] Signal after change for:

[0085]

[0086] in This indicates the error in the magnitude of the voltage change. This indicates the fixed phase offset of the system.

[0087] The core of IQ demodulation is to multiply the signal with two orthogonal local oscillator signals and filter out high-frequency components. Here, the two orthogonal local oscillator signals have equal amplitudes and a phase difference of 90°.

[0088] For the local oscillator signal Multiplying them together gives:

[0089]

[0090] in, Indicates the original An abbreviation for voltage or current, which is the measured voltage or current signal detected by a voltage or current probe detection system.

[0091] We can obtain the product-to-sum formula for trigonometric functions:

[0092]

[0093] Then, high-frequency components are filtered out by a low-pass filter and... The DC signal can be obtained after representing the total gain. :

[0094]

[0095] For the local oscillator signal Multiplying them together gives:

[0096]

[0097] We can obtain the product-to-sum formula for trigonometric functions:

[0098]

[0099] Then, high-frequency components are filtered out by a low-pass filter and... The DC signal can be obtained after representing the total gain. :

[0100]

[0101] This represents the signal obtained after filtering out high-frequency signal components using a low-pass filter. Indicating targeting The process of filtering out high-frequency components from a signal by passing it through a low-pass filter, where Q represents the DC signal obtained after filtering out the high-frequency components, and I(t) represents the signal before passing through the LPF that is related to time t, and the signal after passing through the LPF is independent of time t because the high-frequency components have been filtered out, leaving only the DC component. Describing a single specific signal requires two dimensions: amplitude and phase. After converting the signal into the complex domain, its two dimensions can also be described.

[0102] This represents the error in amplitude change caused by the voltage passing through a fixed circuit system. This refers to the fixed phase shift of the system caused by the sampled voltage or current signal passing through a fixed circuit system. This represents the total gain generated by the entire circuit, that is, the normalized gain of the circuit amplitude.

[0103] The DC signals I and Q can represent the original signals with amplitude and phase shifts generated by the coupling circuit, satisfying the following relationship:

[0104]

[0105]

[0106] in This represents a complex number, where j represents the imaginary unit. This represents the addition of a real number of I and an imaginary number of Q.

[0107] Original voltage signal and the original current signal Since there exists a real number field, it can be transformed to the complex number field using the Hilbert transform;

[0108]

[0109] ;

[0110] A signal in the complex domain can be converted back to a signal in the real domain by taking its real part.

[0111]

[0112]

[0113] Original voltage signal The generated amplitude and phase offset signals and the original current signal The generated amplitude and phase offset signals We can obtain:

[0114]

[0115]

[0116] Regarding the actual impedance yes:

[0117]

[0118] Impedance that can be obtained through testing It is:

[0119]

[0120] Introducing calibration factors It can be confirmed and The following relationship exists:

[0121]

[0122]

[0123] Calculate the four fixed quantities in the calibration factor. , , , The calibration factor can then be calculated, where, This indicates the amplitude error of the voltage output signal. This indicates the phase shift of the voltage output signal. This indicates the amplitude error of the current output signal. This indicates the phase shift of the current output signal, specifically... This indicates the amplitude error between the actual voltage amplitude and the measured voltage amplitude obtained after the voltage signal is acquired through the voltage and current detection probe system and then demodulated by IQ. This indicates the phase error between the actual voltage amplitude and the measured voltage phase, which is reflected in the voltage signal acquired after passing through the voltage and current detection probe system and then demodulated by IQ. This indicates the amplitude error between the actual current amplitude and the measured current amplitude, after the current signal is acquired through the voltage and current detection probe system and then demodulated by IQ. This indicates the phase error between the actual current amplitude and the measured current phase, reflected in the current signal acquired after passing through the voltage and current sensing probe system and then demodulated by IQ. The actual impedance can then be obtained by calculating the calibration factor. With test impedance The relationship, and the test impedance is determined by what can be read. , , , We obtained, among which, This represents the DC component I read from the voltage-coupled signal after IQ demodulation and then passing through an ideal filter. This represents the DC component Q of the voltage-coupled signal, after IQ demodulation and passing through an ideal filter. This represents the DC component I read from the current-coupled signal after IQ demodulation and then passing through an ideal filter. This refers to the DC component Q of the signal after it has been current-coupled, demodulated by IQ, and then passed through an ideal filter. Specifically... This represents the DC signal I value obtained after the voltage signal is acquired through the voltage and current detection probe system and then demodulated by IQ. This represents the DC signal Q value obtained after the voltage signal is acquired through the voltage and current detection probe system and then demodulated by IQ. This represents the DC signal I value obtained after the current signal is collected by the voltage and current detection probe system and then demodulated by IQ. This refers to the DC signal Q value obtained after the current signal is acquired through the voltage and current sensing probe system, and then demodulated by IQ. This value is determined by the calibration readings and the inherent calibration factor coefficient within the system. Calculate the final true impedance.

[0124] Impedance calibration: This refers to the process of applying power to a known impedance, passing the voltage and current signals through a voltage and current sensing probe system, demodulating the signals, and then obtaining the DC signal I and DC signal Q values ​​through IQ demodulation. These are then summed using complex summation. and Satisfy the following formula:

[0125]

[0126]

[0127] , , , The corresponding measured voltage and current waves, after passing through the voltage and current detection probe system, are used to acquire voltage and current signals. These signals are then demodulated using IQ modulation to obtain the DC signal I and DC signal Q values. and This is the amplitude reading corresponding to the actual impedance value, and its ratio is any impedance. The ratio of is applied to any measured impedance including error.

[0128]

[0129] Then the system error factor:

[0130]

[0131] Therefore, the calibration factor can be derived from the data:

[0132]

[0133] Therefore, when faced with unknown impedance, one can read... , , , Calculate And the corresponding and It satisfies the following formula.

[0134] This represents the value read from the voltage-coupled signal after IQ demodulation. This represents the value read from the voltage-coupled signal after IQ demodulation. This represents the value read from the current-coupled signal after IQ demodulation. This represents the value read from the current-coupled signal after IQ demodulation.

[0135] Specifically, This represents the DC signal I value obtained after the voltage signal is acquired through the voltage and current detection probe system and then demodulated by IQ. This represents the DC signal Q value obtained after the voltage signal is acquired through the voltage and current detection probe system and then demodulated by IQ. This represents the DC signal I value obtained after the current signal is collected by the voltage and current detection probe system and then demodulated by IQ. This represents the DC signal Q value obtained after the current signal is collected by the voltage and current detection probe system and then demodulated by IQ.

[0136]

[0137]

[0138] Simultaneously calculate their ratio:

[0139]

[0140] The final impedance then satisfies the formula:

[0141]

[0142] This is the error factor introduced through data derivation mentioned above. By calibrating with any impedance, the corresponding error factor is determined, and the corresponding true impedance is calculated based on the error factor reading.

[0143] Example:

[0144] For a given set of load values, after power is applied, a voltage wave connected to the load conductor can be coupled out using a coupler. With current waves A small segment of power, that is, the coupled measured signal voltage wave and current wave signal. At this point, the actual load impedance can be calculated using the voltage and current waveforms, satisfying the formula:

[0145]

[0146] When a high-frequency signal propagates along a transmission line and encounters an open-circuit endpoint, the electromagnetic wave undergoes total internal reflection. At this point, the incident and reflected waves superimpose to form a standing wave, causing the current and voltage to exhibit a specific distribution pattern. The measured voltage and current signals are then coupled out. This power will equivalently reflect the coupled signal, and there is an error factor. The measured impedance value follows the formula below:

[0147]

[0148] At this point, by changing the load value, the following IQ values ​​are obtained from the simulation output of the IQ demodulation impedance calculation system, as shown in Table 1:

[0149] Table 1

[0150]

[0151] After setting up the test system, a known load impedance is connected, and the voltage and current waves with amplitude and phase shifts generated by the coupling circuit are tested. Then, after passing through the IQ demodulation system, two sets of corresponding IQ values ​​are collected, which meet the requirements of the table above.

[0152] Then when When using the precise load calibration component 50+j*0, we can obtain:

[0153]

[0154] Based on this data, begin calculating the error calibration factor. It follows the formula as follows:

[0155]

[0156] Then the following relationship exists between the calculation formulas at this time:

[0157]

[0158] Then calibration factor real part With the imaginary part They respectively satisfy:

[0159]

[0160]

[0161] Based on the above data, the calibration factor can be calculated. real part With the imaginary part Respectively with calibration impedance The product of the two satisfy the following equation:

[0162]

[0163]

[0164] Therefore, the calibration factor can be real part With the imaginary part The calibration factor is calculated using the following formula. real part With the imaginary part Specific values:

[0165]

[0166]

[0167] Therefore, it is possible to calculate the impedance when facing an unknown impedance. But the parameters are known. , , , When the following equation is satisfied:

[0168]

[0169]

[0170] Therefore, the impedance is unknown. The solution can satisfy the following equation:

[0171]

[0172] but The real and imaginary parts satisfy the formula:

[0173]

[0174]

[0175] The load value can be calculated in the end. : .

[0176] Based on the above system test values, the calibration calculation results satisfy the IQ demodulation impedance calculation system simulation values, which are then substituted into Table 2:

[0177] Table 2

[0178]

[0179] It is evident that after calibration using the IQ demodulation impedance detection system with the error factor, the calculated value has a very small error compared to the actual value, which can meet the impedance detection and calculation requirements of real-world systems.

[0180] To calibrate the impedance for actual unknown impedance;

[0181] The complex impedance can be obtained by the complex ratio of the coupled voltage wave to the current wave, while also considering the pure load impedance. The final value can be obtained:

[0182]

[0183] Due to the connection of pure load impedance It can satisfy:

[0184]

[0185]

[0186] If at this time both the voltage amplitude and the current amplitude are unit values, that is... , If this holds true, both the voltage phase and the current phase will have no frequency deviation, i.e. , It always holds true, that is, it satisfies:

[0187]

[0188] The signal calculated at this time The following relationship must be satisfied:

[0189]

[0190] The amplitude error and phase shift of the system can be obtained through calibration calculations:

[0191]

[0192]

[0193] Connecting pure load impedance The amplitude error and phase offset are calculated using the two sets of IQ values ​​obtained from the measurement, thereby completing the impedance calibration.

[0194] Load calibration element Input and error calibration.

[0195] After calibration, it is finally connected to the IQ demodulation impedance detection system and compared with the original voltage signal. With the original current signal Two sets of IQ values ​​with a corresponding relationship , , , It contains variables , , , If the error is within a certain range, then the voltage and current signal readings after IQ demodulation satisfy the following relationship:

[0196]

[0197]

[0198] Load calibration element Substituting into the circuit, if at this time... and All are unit values, that is, they satisfy... , , , If the condition holds true, then since it is a purely resistive element, the above equation becomes:

[0199]

[0200]

[0201] Based on the read value , , , All unknowns in the above equation can be determined by reverse calibration, thus satisfying:

[0202]

[0203]

[0204]

[0205]

[0206] Therefore, regarding satisfying , , , The system calibrates the specific values ​​of the amplitude and phase deviations of the reference value, storing them as specific system values, and simultaneously writes their ratio as a calibration factor. The calibration factor... The calibration result is:

[0207]

[0208] For an unknown impedance At that time, the above four variables , , , Save it, within the same system, by reading , , , The final impedance is obtained, and the measured value corresponding to the reading at this point satisfies the following relationship:

[0209]

[0210]

[0211] This impedance includes unknown impedance amplitude and frequency deviations. Therefore, the deviations of the unknown impedance need to be calibrated into the final impedance result of the test. for:

[0212]

[0213] Using the methods described above, the final result is calibrated, and the reading is found. , , , With final impedance The corresponding relationship.

[0214] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0215] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for measuring and calibrating impedance based on IQ demodulation calculation, characterized in that, include: The voltage and current signals in the voltage-current coupler circuit are measured by coupling the voltage and current signals to obtain the original current signal. and the original voltage signal ; The impedance value in the circuit is obtained through standard components or measurement methods and is used as the known impedance. Based on the known impedance and the original current signal Original voltage signal This yields two sets of DC signal I and DC signal Q values ​​that reflect voltage and current waves, respectively. Based on the DC signal I and DC signal Q values ​​that reflect voltage and current waves and the corresponding known impedance, the error M that affects the final calculated impedance is calculated, and the error M brought by the impedance detection system of IQ demodulation calculated impedance is set as the standard calibration factor of a single system. Read the numerical value with errors, and calculate the final standard impedance value by correcting the errors caused by the reading value; Also includes test impedance Test impedance The result is obtained by dividing the voltage wave and current wave with amplitude and phase shifts that are coupled out through the coupling circuit after passing radio frequency power through a known impedance. Introducing calibration factors It can be confirmed and The following relationship exists to determine the actual impedance. : Where M is the calibration factor, and... This indicates the amplitude error of the voltage output signal. This indicates the phase shift of the voltage output signal. This indicates the amplitude error of the current output signal. This indicates the phase shift of the current output signal.

2. The method for measuring and calibrating impedance based on IQ demodulation as described in claim 1, corresponding to the DC signal. Values ​​and DC signals Value through the original voltage signal Original current signal It can be obtained by mixing with a signal of the same frequency and then passing it through a low-pass filter; Specifically: DC signal With DC signal Component calculation and representation of the original signal: The DC signals I and Q can represent the original signals with amplitude and phase shifts generated by the coupling circuit, satisfying the following relationship: in: This represents the true amplitude of the original signal. Represents the true phase of the original signal. I(t) represents the signal obtained after filtering out high-frequency signal components through a low-pass filter. The signal before passing through the LPF is related to time t. After passing through the LPF, the high-frequency components are filtered out, and the signal is independent of time t, leaving only the DC component. To describe a single specific signal, two dimensions, amplitude and phase, are required. After converting the signal into the complex domain, its two dimensions can also be described. This represents the error in amplitude change caused by the voltage passing through a fixed circuit system. This refers to the fixed phase shift of the system caused by the sampled voltage or current signal passing through a fixed circuit system. This represents the total gain produced by the entire circuit. This represents a complex number, where j represents the imaginary unit. This represents the addition of a real number of I and an imaginary number of Q.

3. The method for measuring and calibrating impedance based on IQ demodulation calculation according to claim 2, characterized in that, DC signal Obtaining: The original coupled voltage signal is: ； After passing through the circuit system, both the phase and amplitude will be incorrect. After passing through the coupler that couples the voltage wave signal and the current wave signal, both the amplitude and phase of the original signal will change. This can be expressed as the signal after the change: ； local oscillator signal Multiplying them together gives: in, Indicates the original Abbreviation; We can obtain the product-to-sum formula for trigonometric functions: High-frequency components are filtered out by a low-pass filter and then... The DC signal can be obtained after representing the total gain. .

4. The method for measuring and calibrating impedance based on IQ demodulation calculation according to claim 3, characterized in that, DC signal Obtaining: For the local oscillator signal Multiplying them together gives: We can obtain the product-to-sum formula for trigonometric functions: Then, high-frequency components are filtered out by a low-pass filter and... The DC signal can be obtained after representing the total gain. .

5. The method for measuring and calibrating impedance based on IQ demodulation calculation according to claim 4, characterized in that, Original voltage signal and the original current signal There exists a real number field; it can be transformed to the complex number field. ； A signal in the complex domain can be converted back to a signal in the real domain by taking its real part. Original voltage signal The generated amplitude and phase offset signals and the original current signal The generated amplitude and phase offset signals We can obtain: For actual impedance It is: The impedance obtained through testing is the test impedance. : This represents the DC component I read from the voltage-coupled signal after IQ demodulation and then passing through an ideal filter. This represents the DC component Q of the voltage-coupled signal, after IQ demodulation and passing through an ideal filter. This represents the DC component I read from the current-coupled signal after IQ demodulation and then passing through an ideal filter. This represents the DC component Q of the current-coupled signal, after IQ demodulation and passing through an ideal filter. This value is then read during calibration, along with the inherent calibration factor coefficient within the system. Calculate the final true impedance.

6. The method for measuring and calibrating impedance based on IQ demodulation calculation according to claim 5, characterized in that, It also includes impedance calibration: calculating the sum of the values ​​obtained by complex number operations after IQ demodulation following the connection of a known calibration impedance. and Satisfy the following formula: , , , The corresponding mapped measured voltage and current waveforms represent two sets of IQ values ​​obtained after IQ demodulation following connection to a known calibration impedance, and these values ​​include errors. This indicates the amplitude error of the voltage output signal. This represents the amplitude error of the current output signal, while and This is the amplitude reading corresponding to the actual impedance value, and its ratio is any impedance. The ratio of is applied to any measured impedance including error. Then the system error factor: Therefore, the calibration factor can be derived from the data: Therefore, when faced with unknown impedance, one can read... , , , Calculate , This represents the value read from the voltage-coupled signal after IQ demodulation. This represents the value read from the voltage-coupled signal after IQ demodulation. This represents the value read from the current-coupled signal after IQ demodulation. This represents the value read from the current-coupled signal after IQ demodulation, and the corresponding value can be calculated. and Satisfy the following formula: Simultaneously calculate their ratio: The final impedance then satisfies the formula: This is the error factor introduced through data derivation mentioned above. By calibrating with any impedance, the corresponding error factor is determined, and the corresponding true impedance is calculated based on the error factor reading.

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