Calibration of impedance measurement equipment

Abstract

A method of calibrating an impedance measurement device (100) for measuring the impedance of a dut (145).

Description

[0001] The present application relates to a method of calibrating an impedance measurement device (100) for measuring the impedance of a dut (145). Background Art

[0002] Impedance spectroscopy is a powerful method for testing and analyzing a wide variety of electrical devices, including batteries and supercapacitors. Impedance measurements are often contaminated by systematic errors such as amplitude and phase tracking, stray inductance, stray capacitance, and unwanted crosstalk. Therefore, properly calibrating the impedance spectrometer is crucial to producing meaningful data.

[0003] As impedance amplitudes decrease and frequencies increase, reliable calibration becomes increasingly difficult. Conventional impedance measurement equipment relies on factory pre-calibration before measurements on the device under test (DUT) begin, and often relies on some form of short-circuit compensation. This calibration typically works well at standard impedances (e.g., 100 mΩ) and signal frequencies (e.g., 1 kHz). However, the situation is different at low impedances (e.g., 100 μΩ) and high signal frequencies (e.g., 10 kHz) (e.g., when testing modern high-power lithium-ion batteries). In addition, the industry is pushing these test limits for very low impedances (e.g., 10 μΩ) and very high signal frequencies (e.g., 100 kHz).

[0004] Currently, factory pre-calibration is compromised by the necessary fixturing (e.g., cabling and / or force and sense traces between the impedance measurement device and the DUT). In addition, existing calibration methods do not use any calibration standards other than short-circuit standards because fully characterized impedance standards are not available. For example, a low-value resistor (e.g., 1 mΩ) is specified for resistance, but not for inductance. Therefore, a complete, absolute, and traceable impedance calibration is not possible, and only relative response calibration can be performed. Although this is sufficient to compare measurements performed by one impedance measurement device, such calibration methods fail when measurements from different impedance measurement devices are compared to each other or when traceable absolute results are required. Therefore, when calibration standards are not available, calibration equipment and procedures are needed to provide reliable calibration even at very low impedances and very high frequencies. Summary of the Invention

[0005] A first aspect of the present invention relates to a method of calibrating an impedance measurement device for measuring low-level impedance of a device under test (DUT), the method comprising:

[0006] performing a short circuit calibration measurement of the impedance measurement device within a predetermined frequency range using a short circuit calibration standard in a case where a force is connected to the sensing trace to obtain short circuit raw data;

[0007] performing a first shunt calibration measurement of the impedance measurement device within the predetermined frequency range using a first shunt calibration standard having a known first resistance value and an unknown first inductance value to obtain first raw data;

[0008] performing a second shunt calibration measurement of the impedance measurement device within the predetermined frequency range using a second shunt calibration standard having a known second resistance value and an unknown second inductance value to obtain second raw data;

[0009] determining first and second complex impedances of the first and second shunt calibration standards, respectively, by calculating the first and second inductance values ​​using the short-circuit raw data and the first and second raw data applied to a specific error model representing a systematic error term of the impedance measurement device; and

[0010] Generic error coefficients of an error model of the impedance measurement device are determined using the first and second complex impedances, the short-circuit raw data, and the first raw data and the second raw data applied to a standard one-port calibration procedure.

[0011] A second aspect of the present invention relates to a method of calibrating an impedance measurement device for measuring low-level impedance of a device under test (DUT) at low and high frequencies, the method comprising:

[0012] determining an offset impedance (Zos) of the impedance measurement device using a first short-circuit calibration standard at an offset zero plane corresponding to a particular error model of the impedance measurement device in response to a test signal sweep over a first predetermined frequency range;

[0013] determining, in response to a test signal sweep over a second predetermined frequency range, a phase angle of a complex scaled value (ks) of a particular error model at a calibration plane for the particular error model using a second short-circuit calibration standard, the calibration plane coinciding with a connection configured to connect to the DUT;

[0014] In response to a test signal sweep over the second predetermined frequency range, measuring a first impedance as first raw data at the calibration plane using a first shunt calibration standard, the first shunt calibration standard having a known first real part and an unknown first imaginary part;

[0015] In response to a test signal sweep over the second predetermined frequency range, measuring impedance as second raw data at the calibration plane using a second shunt calibration standard, the second shunt calibration standard having a known second real part and an unknown second imaginary part;

[0016] determining a magnitude of the complex scaled value (ks) using the first and second known real parts and the first and second original data;

[0017] determining a mutual inductance from a magnetic coupling in a connection configured to connect to the DUT using the first and second known real parts and the first and second raw data;

[0018] determining a first imaginary part versus frequency function (IM(Z(freq))) describing the first imaginary part of the first shunt calibration standard and determining a second imaginary part versus frequency function describing the second imaginary part of the second shunt calibration standard based on the offset impedance (Zos), the complex scaling value (ks), and the mutual inductance (M), wherein the first complex impedance of the first shunt calibration standard includes the known first real part and the described first imaginary part, and the second complex impedance of the second shunt calibration standard includes the known second real part and the described second imaginary part; and

[0019] Using the first and second complex impedances and the first and second raw data, general error coefficients of a general error model of the impedance measurement device are determined.

[0020] A third aspect of the present invention relates to a method of calibrating an impedance measurement device for measuring low-level impedance of a device under test (DUT), the method comprising:

[0021] With the force connected to the sense traces, start with the initial short calibration measurement using the initial short calibration standard.

[0022] performing a short circuit calibration measurement of an impedance measurement device within a predetermined frequency range using a short circuit calibration standard with the force and sense traces connected thereto to obtain short circuit raw data, wherein the initial short circuit calibration standard has different characteristics than the short circuit calibration standard, the different characteristics comprising at least one of a different current path length or a different magnetic coupling between the force and sense traces;

[0023] performing a first shunt calibration measurement of the impedance measurement device within the predetermined frequency range using a first shunt calibration standard having a known first resistance value and an unknown first inductance value to obtain first raw data;

[0024] performing a second shunt calibration measurement of the impedance measurement device within the predetermined frequency range using a second shunt calibration standard having a known second resistance value and an unknown second inductance value to obtain second raw data;

[0025] determining first and second complex impedances of the first and second shunt calibration standards, respectively, by calculating first and second inductance values ​​using the short-circuit raw data and the first and second raw data applied to a specific error model representing a systematic error term of the impedance measurement device;

[0026] determining a universal error coefficient of an error model of the impedance measurement device using the first and second complex impedances, the short-circuit raw data, and the first raw data and the second raw data applied to a standard one-port calibration procedure; and

[0027] A frequency dependent real part of the first shunt calibration standard is determined by comparing the frequency dependent real part to a known frequency dependent function derived from the initial short circuit calibration measurement and the short circuit calibration measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] When with Figure 1 The example embodiments are best understood from the following detailed description when read together. It is emphasized that the various features are not necessarily drawn to scale. In fact, for clarity of discussion, dimensions may be arbitrarily increased or decreased. Where applicable and practical, like reference numerals represent like elements.

[0029] Figure 1 is a simplified block diagram of a test instrument for measuring the impedance of a device under test (DUT), according to a representative embodiment.

[0030] Figure 2 is in accordance with the instructions of the representative implementation scheme and Figure 1 Simplified circuit diagram of the impedance measurement device corresponding to the specific error model.

[0031] Figure 3 is a simplified flow chart for determining the calibrated impedance of a DUT, according to a representative embodiment.

[0032] Figure 4A Included are graphs showing examples of the impedance of a calibration standard and the calibrated impedance of a DUT determined according to representative embodiments.

[0033] Figure 4B Included are graphs illustrating examples of calibrated impedance of a DUT as a function of frequency determined according to representative embodiments.

[0034] Figure 5 is a simplified block diagram showing a standard one-port calibration of a test instrument. DETAILED DESCRIPTION

[0035] In one embodiment of the method of the first aspect of the present invention, determining the first and second complex impedances of the first shunt calibration standard and the second shunt calibration standard comprises:

[0036] determining a model error coefficient according to the specific error model using the first original data and the second original data; and

[0037] The first inductance and the second inductance values ​​are calculated using the model error coefficient and the first raw data and the second raw data.

[0038] In one embodiment of the method of the first aspect of the present invention, each of the first shunt calibration standard and the second shunt calibration standard has a low level impedance between about 1 micro-ohm and about 100 ohms.

[0039] In a specific embodiment of the method according to the first aspect of the present invention, the model error coefficients include an offset impedance, a complex scaling value, and a mutual inductance corresponding to the impedance measurement device.

[0040] In a more specific embodiment, the method further comprises:

[0041] In the absence of the force and sense traces being connected, starting an initial short circuit calibration measurement of the impedance measurement device using an initial short circuit calibration standard to obtain initial short circuit raw data; and

[0042] The offset impedance is calculated using the initial short circuit calibration measurement.

[0043] In a more specific embodiment, the method further comprises:

[0044] The initial short circuit calibration measurement is performed beginning with the force and sense traces connected using the initial short circuit calibration standard, wherein the initial short circuit calibration standard has different characteristics compared to the short circuit calibration standard, the different characteristics comprising at least one of a different current path length or a different magnetic coupling between the force and sense traces.

[0045] In a specific embodiment of the method involved in the first aspect of the present invention, the method further comprises:

[0046] connecting the DUT to the impedance measurement device via the force and sense trace connections;

[0047] measuring the impedance of the DUT over at least a portion of the predetermined frequency range; and

[0048] A calibrated complex impedance of the DUT is determined using the measured impedance and the determined universal error coefficient.

[0049] In a specific embodiment of the method involved in the first aspect of the present invention, the first raw data includes a first measured impedance disturbed by a systematic error, and the second raw data includes a second measured impedance disturbed by a systematic error.

[0050] In a specific embodiment of the method involved in the first aspect of the present invention, the standard one-port calibration procedure is based on a linear network model. In a more specific embodiment, the linear network model includes linear network parameters including ABCD parameters, S parameters and / or Z parameters.

[0051] In a specific embodiment of the method involved in the first aspect of the present invention, the error model includes a single-port error model using one of a four-wire connection method, a two-wire connection method, an IV method, or an auto-zero bridge method.

[0052] In a specific embodiment of the method according to the second aspect of the present invention, the universal error model comprises a standard one-port calibration procedure.

[0053] In a specific embodiment of the method involved in the second aspect of the present invention, the method further comprises:

[0054] connecting the DUT to the impedance measurement device on the calibration plane of the specific error model;

[0055] performing an impedance measurement of the DUT over at least a portion of the first and second predetermined frequency ranges; and

[0056] A calibrated complex impedance of the DUT is determined using the impedance measurement and the determined universal error coefficients of the universal error model.

[0057] In a more specific embodiment, the geometry of each of the first shunt calibration standard and the second shunt calibration standard matches the geometry of the DUT.

[0058] In a specific embodiment of the method involved in the third aspect of the present invention, the method further comprises:

[0059] The resistance of one of the first and second shunt calibration standards is measured by a direct current (DC) signal or a low frequency signal in the range of about 1 mHz to about 1 kHz.

[0060] In the detailed description below, example embodiments disclosing specific details are set forth for purposes of explanation, not limitation, to provide a more complete understanding of the embodiments according to the present teachings. However, it will be apparent to those skilled in the art having the benefit of this disclosure that other embodiments according to the present teachings that deviate from the specific details disclosed herein are still within the scope of the appended claims. In addition, known devices and methods are not described here in detail so as not to obscure the description of the example embodiments. Such methods and devices are clearly within the scope of the present teachings.

[0061] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting. The defined terms are to be given the technical and scientific meanings of the defined terms as commonly understood and accepted in the art of the present teachings.

[0062] Unless otherwise specified, when a first element is referred to as being connected to a second element, this includes the possibility that one or more intermediate elements may be used to connect the two elements to each other. However, when a first element is referred to as being directly connected to a second element, this only includes the possibility that the two elements are connected to each other without any intermediary or intermediate devices. Similarly, when a signal is referred to as being coupled to an element, this includes the possibility that one or more intermediate elements may be used to couple the signal to the element. However, when a signal is referred to as being directly coupled to an element, this only includes the possibility that the signal is directly coupled to the element without any intermediary or intermediate devices.

[0063] As used in this specification and the appended claims, the terms "a," "an," and "the" include singular and plural referents unless the context clearly indicates otherwise. Thus, for example, reference to "a device" includes references to both one device and multiple devices. As used in the specification and the appended claims, and in addition to their ordinary meaning, the terms "substantially" or "substantially" mean within an acceptable limit or degree. As used in the specification and the appended claims, and in addition to their ordinary meaning, the term "approximately" means within an acceptable limit or amount to a person skilled in the art. For example, "approximately the same" means that a person of ordinary skill in the art would consider the items being compared to be the same.

[0064] Relational terms such as "above," "below," "top," and "bottom" may be used to describe the relationship between different elements as shown in the accompanying drawings. These relational terms are intended to encompass different orientations of their elements in addition to the orientations depicted in the accompanying drawings. For example, if an apparatus (e.g., a signal measuring device) depicted in a drawing is inverted relative to the view in the drawing, an element described as being "above" another element would now be below the element. Similarly, if the apparatus is rotated 90° relative to the view in the drawing, an element described as being "above" or "below" another element would now be "adjacent" to the other element; where "adjacent" means adjacent to the other element or having one or more layers, one or more materials, structures, etc. between the elements.

[0065] Generally, according to various embodiments, full impedance calibration of impedance measurement equipment (such as a network analyzer, impedance analyzer, LCR meter, or other spectrometer) can be performed without fully characterized calibration standards. In other words, calibration can be performed using low-value resistors and short-circuit standards, where only the real part (resistance) of the low-value resistors is specified. Therefore, full impedance calibration can be performed directly at the DUT connector in the impedance domain.

[0066] According to each embodiment, the impedance measuring device is calibrated simply and reliably. The calibration process is very fast and can be used not only for research and development, but also for production environments (such as battery pack production testing). The accuracy of the calibration process depends only on partially known shunt calibration standards (resistors), wherein the real part (resistance value) is known and the imaginary part (inductance value) is unknown. Even with relatively cheap calibration standards, this can effectively predict the uncertainty of subsequent impedance measurements and produce reliable and repeatable results. In each embodiment, the calibration standard can be integrated into the impedance measuring device, and the integrated calibration standard can be automatically selected using a multiplexer. The resistance of the calibration standard can also be measured under direct current, and the frequency behavior with appropriate EM modeling is taken into account.

[0067] The frequency-dependent real part of the shunt resistor (shunt calibration standard) can also be determined by comparing the frequency-dependent real part with a known frequency-dependent function. For example, the shunt resistor can be measured by an impedance measuring device, as described below. Subsequently, for example, a first short circuit standard and a second short circuit standard are measured with first and second short circuit standards having different characteristics (e.g., such as different current path lengths or different magnetic coupling between the force and sense traces). The short circuit standard measurements can be used to construct a signal of known frequency response, for example by subtraction to provide a difference signal. The constructed signal can have a fixed phase angle and an amplitude that increases linearly with frequency. In addition, the constructed signal can be used to determine the transfer function TF of the impedance measuring device, for example, as follows: Where |TF| is the amplitude (absolute value) of the transfer function, Im(difference signal) is the imaginary part of the difference signal, ω is the angular frequency, and c is a constant. The frequency-dependent real part of the shunt resistor can be determined by taking the real part of the measured frequency-dependent raw impedance of the resistor and dividing or multiplying it by the determined transfer function TF. The remaining constant c can be determined by resistance measurements at low frequencies in the range of about 1 mHz to about 1 kHz or at direct current (DC). This results in a fully automatic self-calibration.

[0068] Figure 1 FIG2 is a simplified block diagram of an impedance measurement apparatus for measuring the impedance of a device under test (DUT) according to a representative embodiment. The calibration procedure calibrates low-level impedance measurements, for example, within a frequency range from 1 microhertz up to approximately 1 MHz, and within a range from approximately 1 microohm up to approximately 100 ohms. In general, embodiments are applicable to various types of test instruments for measuring impedance, including, for example, IV methods, auto-zero bridges, two-wire connections, or four-wire connections, and implementations of current or voltage source excitation. Current source excitation is also known as constant current measurement, while voltage source excitation is also known as constant potentiostat measurement.

[0069] refer to Figure 1 , an impedance measurement device 100 is shown connected to a DUT 140 via a force and sense trace (or test fixture) 170 to measure the impedance of the DUT 140. The impedance measurement device 100 includes an excitation current source 110, a current measurement circuit 120, and a voltage measurement circuit 130. The impedance measurement device 100 can be, for example, a network analyzer, a spectrum analyzer, an impedance analyzer, an oscilloscope combined with a signal generator, a general-purpose digitizer combined with a generator, a lock-in amplifier combined with built-in or dedicated hardware of a generator or other impedance spectrometer that may include an analog-to-digital converter (ADC), a digital-to-analog converter (DAC), an operational amplifier, or digital signal processing (DSP) or field-programmable gate array (FPGA) technology.

[0070] The impedance measurement device 100 may also include a processing unit 180 that is connected (wired or wirelessly) to each of the excitation current source 110, the current measurement circuit 120, and the voltage measurement circuit 130 to control various operations and perform measurements. The processing unit may include one or more computer processors, DSPs, FPGAs, application specific integrated circuits (ASICs), or a combination thereof, using any combination of hardware, software, firmware, hard-wired logic circuits, or a combination thereof. The processing unit 180 may include its own processing memory (e.g., volatile and / or non-volatile memory) for storing computer-readable code that enables the various functions described herein to be performed. For example, the processing memory may store software instructions / computer-readable code that can be executed by the processing unit (e.g., a computer processor) for performing some or all aspects of the functions and methods described herein, including the following references. Figure 3 The various steps of the method described herein.Memory described herein can be implemented by random access memory (RAM) and read-only memory (ROM) of any number, type and combination, and various types of information (computer program and software algorithm that can be performed by MIMO target simulator 130, such as discussed below) can be stored, and for example, the data of antenna pattern / spacing and driving scene for DUT 101.Various types of ROM and RAM can comprise the computer-readable storage medium of any number, type and combination, such as disk drive, electrically programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), register, hard disk, removable disk, magnetic tape, compact disk read-only memory (CD-ROM), digital versatile disk (DVD), floppy disk, blue-ray disk, universal serial bus (USB) driver or other forms of storage medium as known in the art, these computer-readable storage media are tangible non-transient storage media (for example, compared with transient propagation signal).

[0071] The excitation current source 110 responds to the input signal I 输入 (indicated as a current signal for illustration purposes), an output current I is provided to the DUT 140 via a first connecting cable 171 (eg, a coaxial cable) of the force and sense trace 170. 输出 (excitation signal). The DUT 140 includes a DUT impedance 145 connected to a first connection cable 171 and a second connection cable 172 (e.g., coaxial cables) connected to the force and sense trace 170. The current measurement circuit 120 is also connected to the DUT 140 via the first connection cable 171 and is configured to enable measurement of the DUT current I through the DUT impedance 145. d The voltage measurement circuit 130 is connected to the DUT 140 via the second connection cable 172 and is configured to enable measurement of the DUT voltage V across the DUT impedance 145.d .

[0072] More specifically, the excitation current source 110 includes a first amplifier 111 having a non-inverting input connected to a digital-to-analog converter (DAC) 116 to receive an input signal I 输入 , and connected to the inverting input of the feedback loop to ensure that the output signal I 输出 (Excitation signal) accurately follows the input signal I from DAC 116 输入 Input signal I 输入 For example, it can be a frequency swept sinusoidal signal, but other types of waveforms, such as band-limited noise, multi-sine wave signals, or pseudo-random bit sequence (PRBS) signals, can also be incorporated. The first amplifier 111 can be, for example, a linear bipolar amplifier, but other technologies, such as switching converters and interleaved switching converters, can be incorporated without departing from the scope of the present teachings. The excitation current source 110 also includes first and second transistors 113 and 114 connected to the output of the first amplifier 111, and a resistor 115 connected at one end between the sources of the first and second transistors 113 and 114 and at the other end to the first connection cable 171. The voltage across the resistor 115 is input to the second amplifier 112 (feedback amplifier), the output of which is provided to the inverting input of the first amplifier 111 to provide a feedback loop, as discussed above. The excitation current source 110 also includes first and second voltage sources 117 and 118 connected between the drains of the first and second transistors 113 and 114. The voltage sources 117 and 118 can be powered, for example, by the grid or any other power source.

[0073] The current measurement circuit 120 includes a shunt resistor 126 connected between the first and second capacitors 117 and 118 at one end and connected to the first connection cable 171 at the other end. The current measurement circuit 120 also includes a third amplifier 123 and an analog-to-digital converter (ADC) 124. The voltage across the shunt resistor 122 is input to the third amplifier 123, and the output of the third amplifier 123 is digitized by the ADC 124 to measure the DUT current I passing through the DUT impedance 145 in the DUT 140. d The digitized current-time signal is processed by a digital signal processing technique such as filtering, fast Fourier transform (FFT), Hilbert transform or correlation analysis, for example, which can be performed by the processing unit 180, thereby obtaining the measured current I m .

[0074] The voltage measurement circuit 130 includes a fourth amplifier 133 and an ADC 134. The voltage from the second connection cable 172 is input to the fourth amplifier 133, and the output of the fourth amplifier 133 is digitized by the ADC 134 to measure the DUT voltage V across the DUT impedance 145 in the DUT 140. d The digitized voltage is used by the processing unit 180 to calculate the voltage vector on the complex plane, thereby obtaining the measured voltage V m The measured current I m and the complex measured voltage V m Can be used to determine the measured impedance Z of the DUT 140 m , defined as V m / I m The real impedance Z of DUT 140 d Defined as V d / I d , the actual impedance is the calibration result.

[0075] Figure 1 An overview of systematic errors that occur in the impedance measurement device 100 when measuring low-value impedances of the DUT 140 is provided. Such systematic errors may include gain tracking between the current measurement circuit 120 and the voltage measurement circuit 130, phase and amplitude tracking between the current measurement circuit 120 and the voltage measurement circuit 130, resistance / inductance of the force and sense traces, mutual inductance, and crosstalk between the current measurement circuit 120 and the voltage measurement circuit 130. Embodiments of the calibration process discussed herein correct for these systematic errors.

[0076] Typically, an implementation of the calibration process is structured as a calibration function and a correction function based on a specific error model. The calibration function obtains measured raw data of at least two partially known calibration standards (e.g., the real part is known and the imaginary part is unknown), determines the model error coefficients based on the specific error model, and uses the model error coefficients and the measured raw data to calculate the complex impedance of the at least two partially known calibration standards. Once the calibration standards are fully known from the specific error model, the correction function implements a standard one-port calibration procedure, for example based on an ABCD matrix, to calculate the universal error coefficients for the universal one-port error model. The correction function then obtains the measured impedance Z of the DUT 140. m and universal error coefficients, and determine the true impedance Z of the DUT 140 d , the real impedance is the final calibration result.

[0077] Figure 2 is in accordance with the instructions of the representative implementation scheme and Figure 1 FIG. 1 is a simplified circuit diagram of a specific error model corresponding to the impedance measurement device 100 .

[0078] refer to Figure 2 Specific error model 200 represents the systematic error terms of the impedance measurement device and provides model error coefficients indicative of the systematic error terms. The model error coefficients of specific error model 200 include the mutual inductance M, the offset impedance Zos, and the complex scaling value ks used to determine the imaginary part of each partially known calibration standard.

[0079] The DUT (e.g., DUT 140) is represented by the DUT impedance (or real impedance) Z d Indicates that the DUT impedance is located at the calibration plane 260 of the specific error model 200 used to measure the impedance of the DUT. d The force and sense traces 270 are connected to the (arbitrarily placed) offset zero plane 250, which in the depicted embodiment provides a four-wire connection at connectors A, B, C, and D in the calibration plane 260. The force and sense traces 270 are indicated by first inductors 271 and 272 in the force lines and second inductors 273 and 274 in the sense lines for measuring the DUT current I d and DUT voltage V d The force and sense traces 270 may include connecting cables (eg, first and second connecting cables 171 and 172). When the DUT impedance Z is set during testing d When the first inductor 271 or other impedance is connected to the calibration plane 260, magnetic coupling occurs between the first inductor 271 and 272 and between the second inductor 273 and the second inductor 274, which is represented by the mutual inductance M. It is assumed that the only systematic error between the calibration plane 260 and the offset zero plane 250 is due to the magnetic coupling. Therefore, the measured impedance Z m Any error in will be caused by the voltage induced by the force current into the sense wires. The measured impedance Z m The real part of the (e.g., parallel conductance) should not show significant errors due to the force and sense traces 270, nor should any force current changes due to the sense voltage (e.g., stray capacitance). That is, a particular error model can ignore parasitic capacitance and assume pure inductive coupling between force and sense for the force and sense trace connections. In practice, the DUT impedance Z dThe low impedance level ensures a near-perfect fit for the assumption that the only systematic error is due to magnetic coupling in the force and sense traces 270 between the calibration plane 260 and the offset zero plane 250. Without loss of generality, the short-circuit measurement at the offset zero plane 250 can be replaced by an offset short-circuit measurement at the calibration plane 260 (not shown), where the offset short-circuit standard is a four-wire short-circuit standard with different current path lengths and different magnetic coupling between the force and sense traces 270 or between the terminals of the offset short-circuit standard compared to the short-circuit standard. In this case, the construction of the short-circuit and offset short-circuit standards can ensure that the above assumptions are met. Construction details can include low-loss design, protection against eddy currents, proximity effects, and skin effects.

[0080] Within the impedance measurement device itself (located to the left of the offset zero plane 250), the error model 200 includes Figure 1 The current measurement channel 220 corresponding to the current measurement circuit 120 in Figure 1 The voltage measurement channel 230 corresponds to the voltage measurement circuit 130 in FIG. The current measurement channel 220 is indicated by the current phase tracking function 226 and the current amplitude tracking function 227 and outputs the measured current I m The voltage measurement channel 230 is indicated by a voltage phase tracking function 236 and a voltage amplitude tracking function 237, and outputs the measured voltage V m The arbitrary phase and magnitude responses determined by the current and voltage phase tracking functions 226 , 236 and the current and voltage magnitude tracking functions 227 , 237 are used to determine the complex scaling value ks in the impedance domain. A complex offset impedance Zos is indicated between the current measurement channel 220 and the voltage measurement channel 230 connected at the adder 252 .

[0081] In this way, the impedance measurement device is modeled as an ideal vector ammeter and an ideal vector voltmeter. The systematic error of the impedance measurement device is represented by the model error coefficients including the complex offset impedance Zos, the complex scaling value Ks, and the mutual inductance M. This can eliminate crosstalk between the current measurement channel 220 and the voltage measurement channel 230.

[0082] Figure 3 2 is a simplified flowchart for determining the calibrated impedance of a DUT according to a representative embodiment. Before determining the calibrated (true) impedance of the DUT, the flowchart includes first determining the model error coefficients in a specific error model (e.g., specific error model 200) corresponding to the impedance measurement device. Figure 3 The operations in are controlled and / or performed by one or more processing units or controllers, such as processing unit 180 discussed above.

[0083] refer to Figure 3, the impedance of the first (initial) short circuit calibration standard is measured in block S311. To measure the first short circuit calibration standard, the sense and force lines 270 are disconnected and replaced by the first short circuit calibration standard at the offset zero plane 250 (although the precise location of the connection is not critical). In the depicted embodiment, the first short circuit calibration standard includes a four-wire short circuit connection for connecting to leads A', B', C', and D' on the impedance measurement device, respectively. In an alternative embodiment, the first short circuit calibration standard can be measured with the force and sense traces 270 maintained in place and the offset short circuit calibration standard connected to the calibration plane 260. Offset short circuit calibration is performed for a four-wire short circuit connection connected to leads A, B, C, and D, respectively, wherein the short circuit connection has a different current path length and a different magnetic coupling between the force and sense traces 270 than the second short circuit standard (e.g., as discussed below with reference to block S313). With the first short-circuit calibration standard, the offset impedance of the specific error model 200 is first determined in block S312 based on the raw data from the first short-circuit calibration standard measurement, for example according to the equation, Zos=Zm 短路1 , where Zm 短路1 is the measured raw impedance of the first short calibration standard. More specifically, in response to a test signal sweep over an initial predetermined frequency range, a measurement with desired sweep settings (e.g., the initial predetermined frequency range and number of points) is triggered in block S311, and the acquired raw data is used to calculate the offset impedance Zos in block S312. The calculation may be performed by processing unit 180.

[0084] Blocks S311 and S312 depict initial steps, meaning they do not need to be performed for every DUT measurement. Instead, blocks S311 and S312 can be performed occasionally, such as once every one to twenty weeks, or when a significant hardware change is made to the impedance measurement device 100. The initial predetermined frequency range for measurement should be wide enough to include all expected frequencies for the upcoming DUT measurement to avoid extrapolation, although interpolation is acceptable to some extent.

[0085] The conventional calibration measurement begins at block S313, where the impedance of the second shorted calibration standard is measured at the calibration plane 260 over a predetermined frequency range with the sense and force lines 270 connected. The predetermined frequency range may be the same as or different from the initial predetermined frequency range used for the measurement in block S311. For example, since the type of DUT may be known for the conventional calibration measurement, the predetermined frequency range may be narrower than the initial predetermined frequency range given the specific characteristics of the DUT. The second shorted calibration standard includes a four-wire shorted connection and is connected to leads A, B, C, and D on the force and sense traces 270 in the calibration plane 260, respectively. By definition, the impedance of the second shorted calibration standard is 0+j0 ohms. In block S314, phase tracking is determined in the impedance domain based on the current and voltage phase tracking functions 226 and 236 using the raw data from the second shorted calibration standard measurement. The phase tracking can be determined according to the equation φ 跟踪 =arg(Zm 短路2 -Zos) determines the phase tracking (φ 跟踪 ), where Zm 短路2 is the measured raw impedance of the second short-circuit calibration standard.

[0086] The geometry of the second-section calibration standard matches the geometry of the DUT, as deviations between the two (e.g., differences in contact distance) will result in systematic errors in the DUT measurement. The raw data can also be subsequently used to provide a full one-port calibration, as discussed below.

[0087] Blocks S315 to S319 form a loop in which multiple partially known shunt calibration standards are measured. In order to perform a one-port calibration to determine the common error coefficient in block S321, at least two shunt calibration standards (a first and a second shunt calibration standard) must be measured, therefore, Figure 3 The loop in is executed at least twice. Each shunt calibration standard is a low value resistor with a partially known impedance, meaning that the real part of the impedance (resistance) is known, while the imaginary part of the impedance (inductance) is unknown. Resistors can be relatively inexpensive because they do not need to be used to generate and provide inductance data. In various embodiments, more than two shunt calibration standards (first through Nth shunt calibration standards, where N is a positive integer) can be used to improve calibration by solving an overdetermined calibration problem (e.g., using a least squares error method), as will be apparent to one of ordinary skill in the art.

[0088] In block S315, with the sense and force lines 270 connected, the impedance of the first shunt calibration standard is measured at the calibration plane 260 over a predetermined frequency range. The first shunt calibration standard includes a four-wire shunt for connecting to leads A, B, C, and D in the calibration plane 260, respectively. The raw data from the first shunt calibration standard measurement performed in block S315, and the raw data from the second short calibration standard measurement performed in block S313, are used to determine additional model error coefficients for the specific error model 200. That is, in block S316, based on the raw data from the first shunt calibration standard measurement and the equation: According to the current and voltage amplitude tracking functions 227 and 237, the amplitude tracking (A) is determined in the impedance domain. 跟踪 ), where Zm 分流1 is the measured raw impedance of the first shunt calibration standard, R 分流1 is the known resistance of the first shunt calibration standard. In block S317, the amplitude tracking from block S316 and the phase tracking from block S314 are used to calculate the resistance of the first shunt calibration standard according to the equation and M=j*ω*ks-1*(Zm 短路2 =Zos) determines the complex scaling value ks and the mutual inductance M, where ω is the angular frequency. Using the complex scaling value ks and the mutual inductance M, in block S318, for example, using equation X 分流1 =ks -1 *(Zm 分流1 -Zos)-j*ω*M to determine the imaginary part of the first calibration shunt standard. It is worth noting that the method is for input signals (for example, input signal I 输入 ) acts independently at each frequency.

[0089] In block S319, a determination is made as to whether there is another shunt calibration standard on which measurements are to be performed. When there is another shunt calibration standard to be measured (block S319: Yes), blocks S315 to S318 are repeated as a loop to determine the complex scaling value ks, the mutual inductance M, and the imaginary part of this calibration shunt standard. In an embodiment, each loop results in the calculation of a separate complex scaling value ks and mutual inductance M for each separate shunt imaginary part. In an alternative embodiment, the complex scaling value ks and mutual inductance M from the first loop are reused in subsequent executions and used to calculate the separate imaginary parts. In another alternative embodiment, the complex scaling value ks and mutual inductance M from each loop are collected and processed into a final combined (e.g., averaged) complex scaling value ks and mutual inductance M for the calculation of the separate imaginary parts.

[0090] For example, returning to block S315, with the sense and force lines 270 connected, the impedance of the second shunt calibration standard is measured at the calibration plane 260 within a predetermined frequency. The second shunt calibration standard includes a four-wire shunt for connection to leads A, B, C, and D in the calibration plane 260, respectively. The raw data from the second shunt calibration standard measurement performed in block S315, as well as the raw data from the second short calibration standard measurement performed in block S313, are used to determine additional model error coefficients for the specific error model 200. In block S316, amplitude tracking is determined in the impedance domain based on the raw data from the second shunt calibration standard measurement according to the current and voltage amplitude tracking functions 227 and 237. In block S317, the complex scaling value ks and the mutual inductance M are again determined using the amplitude tracking from block S316 and the phase tracking from block S314. Using the complex scaling value ks and the mutual inductance M, the imaginary part of the second calibration shunt standard is determined in block S318.

[0091] When there are no additional shunt calibration standards to be measured (block S319: No), processing proceeds to block S320. This block is optional (as indicated by the dashed line) and extends the method to frequencies below low frequencies (e.g., <10 Hz). In block S320, a function (or fit) is determined, for example, by fitting a polynomial describing the inductance versus frequency for each shunt calibration standard. The data used to determine the function is limited to a frequency range that excludes frequencies below a certain value (e.g., 10 Hz). For subsequent calibration steps, the inductance data is then derived from the determined function, where the determined function extrapolates the data below a certain frequency value (e.g., 10 Hz). Optional block S320 can be used in situations where the signal-to-noise ratio limit of the impedance measurement device 100 is below a certain frequency (e.g., 10 Hz), since the induced voltage decreases linearly with frequency.

[0092] In block S321, a universal error coefficient (e.g., such as an ABCD error coefficient) is determined using a standard one-port impedance calibration procedure and now fully known calibration standards (including a second short-circuit calibration standard and at least two now fully known shunt calibration standards). In block S322, the DUT impedance of the DUT connected to the force and sense wiring 270 at the calibration plane is measured, replacing the last measured shunt calibration standard. Then, in block S323, the universal error coefficient and the raw data from the measured DUT impedance and the correction function are used to determine the calibrated DUT impedance.

[0093] The correction function is part of any known, standard one-port calibration for calculating universal error coefficients of a universal one-port error model. The standard one-port calibration may be based on linear network modeling, which may include network parameters (e.g., such as ABCD chain parameters, S parameters, and / or Z parameters) that describe the network parameters such as Figure 5 The general error model outlined. That is, Figure 5 is a simplified block diagram showing a standard one-port calibration.

[0094] refer to Figure 5 , the ideal impedance measurement device 510 is connected to the DUT 530 through the error box 520. The error box 520 represents all systematic errors, and the ideal impedance measurement device 510 combined with the error box 520 represents a real (i.e., non-ideal) impedance measurement device. The DUT 530 has a real impedance Z d , you can use Z d =V d / I d To describe, where V d is the DUT voltage across DUT terminals 531 and 532, I d is the DUT current through the DUT 530. More specifically, V d is the voltage across the DUT sensing connector, and I d The voltage across the DUT force connector and the current through the DUT sense connector are not considered, as this does not introduce additional errors due to the nature of low impedance measurements. Error box 520 represents the true impedance Z d With the measured impedance Z m The measured impedance Z m is the reading provided by the ideal impedance measuring device 510, and Z m =V m / I m To describe, where V m is the measured voltage, and I m is the measured current. Thus, the general transformation represented by the error bin 520 can be given, for example, by equations (1) and (2), where A, B, C, and D are the elements in the matrix of the error bin 520:

[0095] V m =A*V d + B*I d (1)

[0096] I m =C*V d + D*I d (2)

[0097] Expressed in terms of measured impedance, equations (1) and (2) are given by equation (3):

[0098] Z m =(A*Z d + B) / (C*Z d + D) (3)

[0099] The error coefficients k1, k2, and k3 are substituted into equation (3), where k1 = C / D, k2 = A / D, and k3 = B / D, as indicated by the calibration equation (4):

[0100] k1*Z m *Z d + Z m = k2 *Z d + k3 (4)

[0101] To solve the error coefficients k1, k2, and k3 in equation (4), it is necessary to solve the equation system (5):

[0102] A*x=b,where and

[0103] The system of equations (5) can be solved exactly using three independent equations corresponding to three calibration standards (e.g., a short calibration standard and two shunt calibration standards such as those discussed above). However, as mentioned above, additional equations corresponding to additional calibration standards (e.g., additional shunt standards) can be added, in which case the system of equations (5) is overdetermined and needs to be solved differently (e.g., by a least squares error method).

[0104] The correction equation (6) is derived from the calibration equation (4) and can be obtained from the measured impedance Z once the error coefficients k1, k2 and k3 are determined from the system of equations (5). m Calculate the true impedance Z d :

[0105] Z d =(Z m - k3) / (k2 - k1*Z m ) (6)

[0106] Figure 4A and Figure 4B is a diagram illustrating an example of determining the calibrated impedance of a DUT according to a representative embodiment. Figure 4A including a graph showing an embodiment of the raw data impedance of a calibration standard and the raw data impedance of a DUT, and Figure 4BIncluded are graphs illustrating examples of calibrated impedance of a DUT as a function of frequency determined according to representative embodiments.

[0107] Figure 4A The diagram includes plotting the real (Re(Z)) and imaginary (Im(Z)) impedances of three calibration standards and a DUT, which in an embodiment is a prismatic battery case with an internal short bar. Assume that the DUT has a low impedance (e.g., less than about 500 μΩ in this example) that is difficult to measure using conventional techniques. The three calibration standards may include a short calibration standard 411 (0Ω), a first shunt calibration standard 412 (1 mΩ), and a second shunt calibration standard 413 (2 mΩ), also in FIG. Figure 4A As discussed above, each of the first and second shunt calibration standards 412 and 413 is partially known because only the real part (resistance) is provided. The short circuit calibration standard 411 includes terminals 411a and 411b for connecting to an impedance measurement device (e.g., impedance measurement device 100) at an offset zero plane and a calibration plane corresponding to a specific error model (e.g., specific error model 200). The first shunt calibration standard 412 includes terminals 412a and 412b, and the second shunt calibration standard 413 includes terminals 413a and 413b for connecting to an impedance measurement device at a calibration plane corresponding to a specific error model. The distance between terminals 411a and 411b must be equal to the distance between the terminals of the DUT. The distance between terminals 412a and 412b can be the same as or different from the distance between terminals 413a and 413b, and can be the same as or different from the distance between the terminals of the DUT. In the depicted embodiment, for purposes of illustration, the distance between terminals 411a and 411b, the distance between terminals 412a and 412b, and the distance between terminals 413a and 413b are equal to one another and also equal to the distance between the terminals of the DUT itself (not shown). This, in part, ensures that the short calibration standard 411 and the first and second shunt calibration standards 412 and 413 have the same geometry as the DUT.

[0108] The raw data measured using each of the short calibration standard 411, the first shunt calibration standard 412, and the second shunt calibration standard 413 connected in place is plotted in a complex plane (eg, a Nyquist plot) to provide Figure 4A In particular, for example, according to the above reference Figure 3 The process discussed determines the imaginary parts of the first and second shunt calibration standards 412 and 413. Trace 404 depicts the complex raw data impedance measurement of the DUT.

[0109] Figure 4BIncluded are two graphs showing calibrated complex impedance measurements of a DUT as a function of the frequency of an excitation signal, wherein the impedance measurement apparatus has been calibrated according to the disclosed embodiments using a short-circuit calibration standard 411 and partially known first and second shunt calibration standards 412 and 413. The upper graph shows a trace 421 plotting the real part of the calibrated DUT impedance (Re(Z)) as a function of frequency, and the lower graph shows a trace 422 plotting the imaginary part of the calibrated DUT impedance (Im(Z)) as a function of frequency. In the depicted embodiment, for example, the DUT is measured over a frequency range of approximately 10 mHz to approximately 30 kHz.

[0110] While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the invention is not limited to the disclosed embodiments.

[0111] Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude the inclusion of other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

[0112] Although representative embodiments are disclosed herein, those skilled in the art will appreciate that many variations are possible in light of the present teachings and still fall within the scope of the appended claims. Accordingly, the present invention is intended to be limited only by the scope of the appended claims.

Claims

1. A method of calibrating an impedance measurement device for measuring low-level impedance of a device under test, the method comprising: performing a short circuit calibration measurement of the impedance measurement device within a predetermined frequency range using a short circuit calibration standard in a case where a force is connected to the sensing trace to obtain short circuit raw data; performing a first shunt calibration measurement of the impedance measurement device within the predetermined frequency range using a first shunt calibration standard having a known first resistance value and an unknown first inductance value to obtain first raw data; performing a second shunt calibration measurement of the impedance measurement device within the predetermined frequency range using a second shunt calibration standard having a known second resistance value and an unknown second inductance value to obtain second raw data; determining first and second complex impedances of the first and second shunt calibration standards, respectively, by calculating first and second inductance values ​​using the short-circuit raw data applied to a specific error model representing a systematic error term of the impedance measurement device and the first and second raw data; as well as A universal error coefficient of an error model of the impedance measurement device is determined using the first and second complex impedances, the short-circuit raw data, and the first and second raw data applied to a standard one-port calibration procedure.

2. The method according to claim 1, wherein Determining the first complex impedance and the second complex impedance of the first shunt calibration standard and the second shunt calibration standard includes: determining a model error coefficient according to the specific error model using the first original data and the second original data; and A first inductance value and a second inductance value are calculated using the model error coefficient and the first raw data and the second raw data.

3. The method according to claim 1, wherein Each of the first shunt calibration standard and the second shunt calibration standard has a low level impedance between 1 micro-ohm and 100 ohms.

4. The method according to claim 2, wherein The model error coefficients include an offset impedance, a complex scaling value, and a mutual inductance corresponding to the impedance measurement device.

5. The method according to claim 4, further comprising: In the absence of the force and sense traces being connected, performing an initial short circuit calibration measurement of the impedance measurement device using an initial short circuit calibration standard to obtain initial short circuit raw data; as well as The offset impedance is calculated using the initial short circuit calibration measurement.

6. The method according to claim 5, further comprising: The initial short circuit calibration measurement is performed beginning with the force and sense traces connected using the initial short circuit calibration standard, wherein the initial short circuit calibration standard has different characteristics compared to the short circuit calibration standard, the different characteristics comprising at least one of a different current path length or a different magnetic coupling between the force and sense traces.

7. The method according to claim 1, further comprising: connecting the device under test to the impedance measurement device via the force and sense trace connections; measuring the impedance of the device under test over at least a portion of the predetermined frequency range; as well as A calibrated complex impedance of the device under test is determined using the measured impedance and the determined universal error coefficient.

8. The method according to claim 1, wherein The first raw data includes a first measured impedance disturbed by a systematic error, and the second raw data includes a second measured impedance disturbed by a systematic error.

9. The method according to claim 1, wherein The standard one-port calibration procedure is based on a linear network model.

10. The method according to claim 9, wherein The linear network model includes linear network parameters, including ABCD parameters, S parameters and / or Z parameters.

11. The method according to claim 1, wherein The error model includes a one-port error model using one of a four-wire connection method, a two-wire connection method, an IV method, or an auto-zero bridge method.

12. A method of calibrating an impedance measurement device for measuring low-level impedance of a device under test at low and high frequencies, the method comprising: determining an offset impedance (Zos) of the impedance measurement device using a first short-circuit calibration standard at an offset zero plane corresponding to a particular error model of the impedance measurement device in response to a test signal sweep over a first predetermined frequency range; determining, in response to a test signal sweep over a second predetermined frequency range, a phase angle of a complex scaled value (ks) of a particular error model at a calibration plane for the particular error model using a second short-circuit calibration standard, the calibration plane coinciding with a connection configured to connect to the device under test; In response to a test signal sweep over the second predetermined frequency range, measuring a first impedance as first raw data at the calibration plane using a first shunt calibration standard, the first shunt calibration standard having a known first real part and an unknown first imaginary part; In response to a test signal sweep over the second predetermined frequency range, measuring impedance as second raw data at the calibration plane using a second shunt calibration standard, the second shunt calibration standard having a known second real part and an unknown second imaginary part; determining a magnitude of the complex scaled value (ks) using the known first real part and the known second real part and the first and second raw data; determining a mutual inductance from a magnetic coupling in a connection configured to connect to the device under test using the known first real part and the known second real part and the first and second raw data; determining a first imaginary part versus frequency function (IM(Z(freq))) describing the first imaginary part of the first shunt calibration standard and determining a second imaginary part versus frequency function describing the second imaginary part of the second shunt calibration standard based on the offset impedance (Zos), the complex scaling value (ks), and the mutual inductance (M), wherein the first complex impedance of the first shunt calibration standard includes the known first real part and the described first imaginary part, and the second complex impedance of the second shunt calibration standard includes the known second real part and the described second imaginary part; as well as A general error coefficient of a general error model of the impedance measurement device is determined using the first and second complex impedances and the first and second raw data.

13. The method according to claim 12, wherein: The general error model includes a standard one-port calibration procedure.

14. The method according to claim 12, further comprising: connecting the device under test to the impedance measurement device on the calibration plane of the specific error model; performing an impedance measurement of the device under test over at least a portion of the first predetermined frequency range and the second predetermined frequency range; as well as A calibrated complex impedance of the device under test is determined using the impedance measurements and the determined universal error coefficients of the universal error model.

15. The method according to claim 14, wherein The geometry of each of the first shunt calibration standard and the second shunt calibration standard matches the geometry of the device under test.

16. A method of calibrating an impedance measurement device for measuring low-level impedance of a device under test, the method comprising: With the force connected to the sense traces, start with the initial short calibration measurement using the initial short calibration standard. performing a short circuit calibration measurement of an impedance measurement device within a predetermined frequency range using a short circuit calibration standard with the force and sense traces connected thereto to obtain short circuit raw data, wherein the initial short circuit calibration standard has different characteristics than the short circuit calibration standard, the different characteristics comprising at least one of a different current path length or a different magnetic coupling between the force and sense traces; performing a first shunt calibration measurement of the impedance measurement device within the predetermined frequency range using a first shunt calibration standard having a known first resistance value and an unknown first inductance value to obtain first raw data; performing a second shunt calibration measurement of the impedance measurement device within the predetermined frequency range using a second shunt calibration standard having a known second resistance value and an unknown second inductance value to obtain second raw data; determining first and second complex impedances of the first and second shunt calibration standards, respectively, by calculating first and second inductance values ​​using the short-circuit raw data applied to a specific error model representing a systematic error term of the impedance measurement device and the first and second raw data; determining a universal error coefficient of an error model of the impedance measurement device using the first and second complex impedances, the short-circuit raw data, and the first and second raw data applied to a standard one-port calibration procedure; and A frequency dependent real part of the first shunt calibration standard is determined by comparing the frequency dependent real part to a known frequency dependent function derived from the initial short circuit calibration measurement and the short circuit calibration measurement.

17. The method according to claim 16, further comprising: The resistance of one of the first shunt calibration standard and the second shunt calibration standard is measured by a direct current (DC) signal or a low frequency signal in the range of 1 mHz to 1 kHz.

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