# Battery Impedance Spectroscopy Embedded Measurement System

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## Abstract

**:**

## 1. Introduction

## 2. Embedded Measurement System

#### 2.1. STM32 Development Kit

#### 2.2. Summing Stage

#### 2.3. Improved Howland Current Pump

#### 2.4. Battery Current Measurement Circuit

#### 2.5. Battery Voltage Measurement Circuit

## 3. Stimulus Generation and System Calibration

#### 3.1. Stimulus Generation

#### 3.2. System Calibration

## 4. Battery Impedance Measurement Results

- (i)
- Fully charge the battery and stop the charge process when the battery charging current is below 10 mA.
- (ii)
- Wait for the battery open voltage to stabilize, setting a threshold of $|d{V}_{\mathrm{BAT}}/dt|$ to terminate the stabilization period (this threshold was set to $0.1\phantom{\rule{3.33333pt}{0ex}}\mathrm{mV}/\mathrm{min}$).
- (iii)
- Perform the impedance measurement procedure, repeating the process 10 times.
- (iv)
- Discharge the battery using a small resistor and end the discharge process when the discharge reaches 25 mAh.
- (v)
- If the battery is fully discharged (detected by the battery internal protection circuit), the procedure ends; otherwise, go back to step (ii).

## 5. Battery Impedance Equivalent Circuit

## 6. Discussion, Conclusions and Future Work

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Block diagram of the embedded measurement system. The developed daughter board includes, besides the shown four main blocks, a power management unit that generates the bipolar DC supply voltage for the analog circuitry.

**Figure 2.**Summing stage circuit. The PWM signals are generated in the STM32 processor, with PWM1 containing the lower-tone frequencies (from 0.5 Hz to 45 Hz) and PWM2 with the higher-tone frequencies (from 50 Hz to 5 kHz). PWM3 is used to generate a DC signal to be subtracted from the other two so that the summing stage output voltage ${v}_{\mathrm{A}}$ does not have a DC component.

**Figure 3.**The improved Howland current pump circuit to convert the multiharmonic processor-generated voltage ${v}_{\mathrm{A}}$ into the current ${i}_{\mathrm{BAT}}$ that is imposed to the battery.

**Figure 4.**Battery current measurement circuit. The AD620 is an instrumentation amplifier whose gain is set with an external swappable resistor. PWM4 is used to add a DC component necessary because of the unipolar range of processor ADC.

**Figure 5.**Battery voltage measurement circuit, where the DC battery voltage is subtracted by the processor adjusted PWM5 and PWM6 signals. The resulting AC component is amplified by the instrumentation amplifier AD620, which is also used to add a DC component (adjust by PWM7) to account for the ADC unipolar range.

**Figure 6.**Measurements of the multiharmonic voltages and corresponding spectrums. (

**a**,

**b**) are the lower-frequency multiharmonic voltage with frequency tones in the 0.5 Hz to 45 Hz range. (

**c**,

**d**) correspond to the higher-range frequency multiharmonic voltage with tones in the 50 Hz to 5 kHz range. The results presented in (

**e**,

**f**) are from the voltage output of the summing stage ${v}_{\mathrm{A}}$, with the complete multiharmonic voltage tones in the 0.5 Hz to 5 kHz range as desired.

**Figure 7.**The calibration coefficients obtained from a set of low-value resistors measured with a reference impedance analyzer (Hioki 3522-50) and with the developed embedded measurement system at the tones that are used to measure the impedance battery. (

**a**) shows the frequency dependence of the amplitude calibration coefficient, and (

**b**) depicts the phase calibration coefficient as a function of the measurement tone frequency.

**Figure 8.**Validation of the calibration procedure using a basic RC parallel circuit, showing the uncalibrated measurement results (thin black lines), the results of the calibration process (thick blue lines) and the reference values (square markers) obtained from the Hioki instrument. (

**a**) represents the impedance magnitude $\left|Z\right|$ as a function of the tone frequency. In (

**b**) the impedance phases are plotted, while in (

**c**) the traditional Nyquist plot, also called the Cole–Cole plot or diagram, shows $-\mathrm{Im}\left(Z\right)$ as a function of $\mathrm{Re}\left(Z\right)$.

**Figure 9.**Impedance measurement results of the LP502248 450 mAh Li-Po battery for three values of the SOC. In (

**a**) the impedance magnitude is plotted as a function of the measurement frequency, while in (

**b**) the impedance phase is depicted. The represented results are the average values obtained from 10 repeated measurements together with uncertainty intervals obtained with a 1.96 coverage factor. The corresponding average Nyquist plots are represented in (

**c**).

**Figure 10.**Average impedance measurement results of the LP502248 450 mAh Li-Po battery for 17 values of the SOC. In (

**a**,

**b**) the impedance magnitude and phase are respectively shown as a function of the SOC and measurement frequency. The corresponding Nyquist plots are shown in (

**c**).

**Figure 11.**Average impedance measurement results of the CA4L 750 mAh Li-ion Canon camera battery for 12 values of the SOC. The impedance magnitude is plotted in (

**a**), while the impedance phase is shown in (

**b**), both as a function of the SOC and measurement frequency. The corresponding Nyquist plots are represented in (

**c**).

**Figure 12.**Average impedance measurement results of the CGAS007 1000 mAh Li-ion Panasonic camera battery for 18 values of the SOC. (

**a**) depicts the impedance magnitude as a function of the SOC and measurement frequency, while (

**b**) is identical for the impedance phase. The results shown in (

**c**) correspond to the Nyquist plots.

**Figure 13.**Battery impedance equivalent circuit. $CPE$ are constant-phase elements whose impedance is defined by two parameters Q and $\alpha $. ${A}_{\mathrm{w}}$ is a Warburg element, and its impedance is defined by parameter ${A}_{\mathrm{w}}$.

**Figure 14.**Equivalent circuit model parameters as a function of the SOC for the Li-Po LP502248 battery. (

**a**) shows the series resistance R and inductance L. (

**b**) depicts the $CP{E}_{1}$ parameters, while (

**c**) includes the $CP{E}_{2}$ values. (

**d**) represents the Warburg parameter, (

**e**) corresponds to the resistor ${R}_{1}$, which is in parallel with $CP{E}_{1}$, and ${R}_{2}$ (in parallel with $CP{E}_{2}$) is represented in (

**f**).

**Figure 15.**Equivalent circuit model parameters as a function of the SOC for the Li-ion CA4L battery. (

**a**) shows the series resistance R and inductance L. (

**b**) depicts the $CP{E}_{1}$ parameters, while (

**c**) includes the $CP{E}_{2}$ values. (

**d**) represents the Warburg parameter, (

**e**) corresponds to the resistor ${R}_{1}$, which is in parallel with $CP{E}_{1}$, and ${R}_{2}$ (in parallel with $CP{E}_{2}$) is represented in (

**f**).

**Figure 16.**Equivalent circuit model parameters as a function of the SOC for the Li-io CGAS007 battery. (

**a**) shows the series resistance R and inductance L. (

**b**) depicts the $CP{E}_{1}$ parameters while (

**c**) includes the $CP{E}_{2}$ values. (

**d**) represents the Warburg parameter, (

**e**) corresponds to the resistor ${R}_{1}$, which is in parallel with $CP{E}_{1}$, and ${R}_{2}$ (in parallel with $CP{E}_{2}$) is represented in (

**f**).

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## Share and Cite

**MDPI and ACS Style**

Cicioni, G.; De Angelis, A.; Janeiro, F.M.; Ramos, P.M.; Carbone, P.
Battery Impedance Spectroscopy Embedded Measurement System. *Batteries* **2023**, *9*, 577.
https://doi.org/10.3390/batteries9120577

**AMA Style**

Cicioni G, De Angelis A, Janeiro FM, Ramos PM, Carbone P.
Battery Impedance Spectroscopy Embedded Measurement System. *Batteries*. 2023; 9(12):577.
https://doi.org/10.3390/batteries9120577

**Chicago/Turabian Style**

Cicioni, Gabriele, Alessio De Angelis, Fernando M. Janeiro, Pedro M. Ramos, and Paolo Carbone.
2023. "Battery Impedance Spectroscopy Embedded Measurement System" *Batteries* 9, no. 12: 577.
https://doi.org/10.3390/batteries9120577