Design of Electrochemical Impedance Spectroscopy (EIS) Measurement System

Circuit functions and advantages

The circuit shown in Figure 1 is an electrochemical impedance spectroscopy (EIS) measurement system used to characterize lithium ion (Li-Ion) and other types of batteries. EIS is a safety perturbation technology used to detect processes occurring inside electrochemical systems. The system measures the impedance of the battery in a certain frequency range. These data can determine the battery's operating state (SOH) and state of charge (SOC). The system uses an ultra-low power analog front end (AFE) designed to stimulate and measure the current, voltage or impedance response of the battery.

Aging will cause degradation of battery performance and irreversible changes in battery chemical composition. The impedance increases linearly with the decrease in capacity. Using EIS to monitor the increase in battery impedance can determine the SOH and whether the battery needs to be replaced, thereby reducing system downtime and maintenance costs.

The battery needs excitation current, not voltage, and the impedance value is very small in the milliohm range. The system includes the necessary circuitry to inject current into the battery and allows calibration and detection of small impedances in the battery.

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Figure 1. Simplified circuit functional block diagram

Circuit description

Battery EIS Theory

Battery is a non-linear system; therefore, detecting a small sample of the battery's I-V curve makes the system exhibit pseudo-linear behavior. In a pseudo-linear system, the sinusoidal output frequency generated by the sinusoidal input is exactly the same, but the phase and amplitude are shifted. In EIS, an AC excitation signal is applied to the battery to obtain data.

The information in EIS is often represented by a Nyquist diagram, but it can also be displayed using a Bode diagram (this circuit note focuses on common formats). In the Nyquist diagram, the negative imaginary component of impedance (y-axis) and the real component of impedance (x-axis) are used for plotting. The different areas of the Nyquist diagram correspond to various chemical and physical processes that occur in the battery (see Figure 2).

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Figure 2: The Nyquist diagram of the battery shows the different areas corresponding to the electrochemical process

These processes are modeled using resistors, capacitors, and a component called Warburg resistance. Warburg resistance is represented by the letter W (described in more detail in the Equivalent Circuit Model (ECM) section). There is no simple electronic component to represent the Warburg diffusion resistance.

Equivalent Circuit Model (ECM)

Equivalent Circuit Model (ECM) uses simple electronic circuits (resistance and capacitance) to simulate electrochemical processes. The model uses a simple circuit to represent a complex process to help analyze and simplify calculations. These models are based on data collected from test batteries. After characterizing the Nyquist plot of the battery, an ECM can be developed. Most commercial EIS software includes an option to create a specific, unique equivalent circuit model to more closely approximate the shape of the Nyquist diagram generated by any particular battery. When creating a battery model, there are four common parameters that represent the chemistry of the battery.

Electrolysis (ohm) resistance—RS

The characteristics of 　　RS are as follows:

corresponds to the resistance of the electrolyte in the battery

Affected by the length of the electrode and the wire used during the test

increases with the aging of the battery

dominates when the frequency is> 1 kHz

Double layer capacitor—CDL

The characteristics of CDL are as follows:

occurs between the electrode and the electrolyte

consists of two parallel layers of opposite charges surrounding the electrode

dominates in the frequency range of 1 Hz to 1 kHz

charge transfer resistance-RCT

Resistance occurs when electrons transfer from one state to another, that is, from a solid (electrode) to a liquid (electrolyte).

Varies with battery temperature and charging status

dominates in the frequency range of 1 Hz to 1 kHz

Warburg (diffusion) resistance—W

represents the resistance to mass transfer, that is, diffusion control

typically exhibits a 45° phase shift

dominates when the frequency is <1 Hz

Table 1 provides the symbols and expressions for each ECM component.

Table 1. ECM components

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build battery ECM

The process of establishing an equivalent circuit model (ECM) is usually based on experience, and various equivalent circuit models need to be used for experiments until the model matches the measured Nyquist diagram.

The following sections will introduce how to create a typical battery model.

Randel circuit model Ohm and charge transfer effect

Randel circuit is a common ECM. The Randel circuit includes electrolyte resistance (RS), double layer capacitance (CDL) and charge transfer resistance (RCT). The double-layer capacitor is parallel to the charge transfer resistance, forming a semicircular analog shape.

The simplified Randel circuit is not only a useful basic model, but also a starting point for other more complex models.

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Figure 3. Randel circuit

Figure 4. Simplified Randel circuit diagram that produces Nyquist diagram

The Nyquist diagram of the simplified Randel circuit is always a semicircle. The electrolyte resistance (RS) is determined by reading the real-axis value at the high-frequency intercept point of the battery characteristics, that is, the high-frequency region is where the line crosses the x-axis on the left side of the graph. In Figure 4, the electrolyte resistance (RS) is the intercept point close to the origin of the Nyquist diagram, which is 30Ω. The real axis value of the other (low frequency) intercept point is the sum of the charge transfer resistance (RCT) and the electrolyte resistance (270 Ω in this example). Therefore, the diameter of the semicircle is equal to the charge transfer resistance (RCT).

Warburg circuit model—diffusion effect

When modeling the Warburg resistance, add the component W and RCT in series (see Figure 5). The increase in Warburg resistance produces a 45° line, which is obvious in the low frequency region of the graph.

Figure 5. Warburg circuit model—diffusion effect

Figure 6. ECM with diffusion effect

Combined Randel and Warburg circuit model

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Some batteries depict two semicircles. One semicircle corresponds to the solid electrolyte interface (SEI). The growth of SEI is caused by the irreversible electrochemical decomposition of the electrolyte. If it is a lithium-ion battery, SEI is formed at the negative electrode as the battery ages. This decomposition product forms a solid layer on the electrode surface.

After the initial SEI layer is formed, electrolyte molecules cannot reach the surface of the active material through the SEI, and react with lithium ions and electrons, thereby inhibiting the further growth of SEI.

combines two Randel circuits to model this Nyquist diagram. Resistance (RSEI) models the resistance of SEI.

Figure 8. Modified Randel circuit model; Nyquist diagram is a lithium-ion battery with obvious SEI

Battery impedance solution using AD5941

AD5941 impedance and electrochemical front-end is the EIS measurement system. AD5941 consists of a low bandwidth loop, a high bandwidth loop, a high analog-to-digital converter (ADC) and a programmable switch matrix.

The low-bandwidth loop is composed of a low-power, dual-output digital-to-analog converter (DAC) and a low-power transimpedance amplifier (TI A). The former can generate VZERO and VBIAS, and the latter can convert the input current into voltage.

low bandwidth loop is used for low bandwidth signals, where the frequency of the excitation signal is lower than 200 Hz, such as battery impedance measurement.

High bandwidth loop is used for EIS measurement. The high-bandwidth loop includes a high-speed DAC that is used to generate an AC excitation signal when making impedance measurements. The high-bandwidth loop has a high-speed TI A that converts high-bandwidth current signals up to 200 kHz into voltages that can be measured by the ADC.

The switch matrix is a series of programmable switches that allow external pins to be connected to the high-speed DAC driver amplifier and the high-speed TI A inverting input. The switch matrix provides an interface for connecting external calibration resistors to the measurement system. The switch matrix also provides flexibility in electrode connection.

The impedance of the battery is usually in the milliohm range, and a calibration resistor RCAL of similar value is required. The 50 m68 RCAL in this circuit is too small for the AD5941 to measure directly. Because RCAL is small, the external gain stage uses AD8694 to amplify the received signal. The AD8694 has ultra-low noise performance and low bias and leakage current parameters, which are critical for EIS applications. In addition, sharing an amplifier between the RCAL and the actual battery helps compensate for errors caused by cables, AC coupling capacitors, and amplifiers.

Excitation signal

AD5941 uses its waveform generator, high-speed DAC (HSDAC) and excitation amplifier to generate sine wave excitation signal. The frequency is programmable, ranging from 0.015 mHz to 200 kHz. The signal is applied to the battery through the CE0 pin and the external Darlington pair transistor configuration, as shown in Figure 9. A current amplifier is required because the upper limit of the current that the excitation buffer can generate is 3 mA. A typical battery requires up to 50 mA.

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Figure 9. Darlington transistor pair

Measure voltage

There are two voltage measurement phases. First, measure the pressure drop across RCAL. Second, measure the battery voltage. The voltage drop across each component is very small in the microvolt range (μV). Therefore, the measured voltage is sent through an external gain stage. The output of the gain amplifier AD8694 is directly sent to the ADC on the AD5941 chip through pins AI N2 and pin AIN3. By using the discrete Fourier transform (DFT) hardware accelerometer, DFT is performed on the ADC data, in which the real and imaginary numbers are calculated and stored in the data FIF O for RCAL voltage measurement and battery voltage measurement. ADG636 multiplexes the battery and RCAL and outputs to the AD8694 gain stage.

The ultra-low charge injection and small leakage current of the ADG636 switch are required to eliminate the parasitic capacitance on the input pin of the AD5941. Since the AIN2 and AIN3 pins are both used for RCAL measurement and battery measurement, the signal path for impedance measurement is proportional.

Calculate unknown impedance (ZUNKNOWN)

EIS adopts proportional measurement method. In order to measure the unknown impedance (ZUNKNOWN), an AC current signal is applied to the known resistance RCAL, and the response voltage VR CAL is measured. Then apply the same signal to the unknown impedance ZUNKNOWN, and measure the response voltage VZUNKNOWN. Perform a discrete Fourier transform on the response voltage to determine the real and imaginary values of each measurement. The unknown impedance can be calculated using the following formula:

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Figure 10.EIS measurement diagram

Circuit evaluation and testing

Overview of the next section CN-0510 Circuit design test procedures and results collection. For complete details on hardware and software settings, please refer to the CN-0510 User Guide.

equipment requirements

PC with USB port and Windows7 or higher.

EVAL-AD5941BATZ circuit board.

EVAL-ADI CUP3029 development board.

CN-0510 Reference Software

USB Type A to mi cro USB cable

Bayonet Neill–Concelman (BNC) connector to connect the grabber / alligator clip

battery (device under test, DUT)

Figure 11. Reference design board

  start using

1. Connect EVAL-AD5941BATZ to EVAL-ADICUP3029 through the Arduino connector.

2. Insert the BNC, and connect the cables on F+, F, S+, and S.

3. Power the development board by connecting the micro USB cable to P10 on the EVAL-ADICUP3029, and plug the other end of the USB cable into your computer.

A. Before connecting the battery, make sure that the development board is powered on to avoid short circuits.

4. Sample firmware from GitHub.

Instructions are provided on the 　　analog.com wiki website.

5. Configure the embedded software as the parameters required by the application.

A. Use AD5940BATStrucTI nit (void) function. (The example is as follows.)

Figure 12. Firmware configuration

A. Use the suggested interactive development environment (IDE) to build the code and transfer the code to the EVAL-ADICUP3029 target board. For installation details, refer to the AD5940 User Guide.

6. Connect the battery as shown in Figure 13. Connect the F+ and S+ leads to the positive terminal of the battery, and connect the S- and F- to the negative terminal of the battery.

7. Press the 3029-RESET button on the EVAL-ADICUP3029.

Figure 13. Complete EIS battery system

Battery test and results

1. Use a program (such as RealTe rm) to open the serial terminal.

2. Configure the baud rate to 230,400.

A. Select the COM port that EVAL-ADICUP3029 is connected to.

3. The measurement results are streamed via UART and can be saved to a file for analysis.

Please note that the calibration function is executed at the beginning of the program. If the excitation frequency is low, it takes at least 4 cycles to capture the waveform. To measure 0.1 Hz, it takes more than 40 seconds to complete.

Please note that the hardware is optimized for frequencies above 1 Hz. Measurements below this value are noisier due to the 1/f noise of the external amplifier.

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Figure 14. The result displayed in the terminal program

Figure 15 shows the Nyquist plot of an example lithium-ion battery measured with the EVAL-AD5941BATZ.

Figure 15. Nyquist plot (scan 1.11 Hz to 50 kHz)