Lithium-ion battery internal resistance and impedance are among the most critical parameters for evaluating battery performance. These parameters serve as key indicators of battery health, operational status, and lifespan. They reflect how easily electrons and ions can move within the electrode materials, making them essential in assessing battery efficiency and reliability. Impedance measurement plays a vital role in battery development, manufacturing, and usage. It helps monitor battery condition, predict remaining life, and even estimate internal temperature by analyzing the impedance angle and mode. Accurate internal resistance measurement is crucial for effective battery management systems and real-world applications.
Common methods for measuring impedance include:
1. Determining the impedance spectrum using the amplitude of the response voltage and excitation current, while calculating the time difference between the two to obtain the impedance angle.
2. The Fast Fourier Transform (FFT) method, which suffers from spectral leakage and the fence effect, leading to inaccuracies in frequency, amplitude, and phase estimation—especially with large phase errors that compromise accuracy.
3. Correlation-based techniques. Due to the small internal resistance of batteries, noise and interference significantly impact measurements. Digital lock-in amplifiers (DLIA), based on correlation detection, effectively suppress noise, enhance signal-to-noise ratio, maintain stable center frequency, and offer narrow bandwidth and high quality factor, enabling precise signal extraction.
In this study, we simulate the impedance measurement process using a digital lock-in amplifier. We then design the overall system, including the architecture and software algorithm improvements. Finally, we perform impedance measurements on a series battery pack and analyze the results along with potential error sources.
**1. Simulation Design of DLIA-Based Impedance Measurement**
**1.1. Algorithm Design**
The battery's response voltage typically remains below 5–10 mV, classifying it as a weak signal that is highly susceptible to noise and interference. The digital lock-in amplifier (DLIA) is central to internal resistance measurement. It leverages correlation detection, where the reference signal frequency aligns with the input signal frequency, while non-synchronous noise is ignored, allowing the useful signal to be extracted from background noise. Based on the fundamental principle of lock-in amplifiers, we propose using the current signal directly as an in-phase reference and generating an orthogonal reference through an algorithm to calculate impedance. The measurement principle is illustrated in Figure 1.
Figure 1: Impedance measurement principle
**1.2. Simulink Simulation Verification Based on DLIA Impedance Measurement** To validate the effectiveness of the digital lock-in amplifier in suppressing noise and improving measurement accuracy, we built a model in Simulink, as shown in Figure 2. The ExcitationSource module generates a sinusoidal excitation current to stimulate the battery, while the battery is modeled using a common second-order RC equivalent circuit. In the DLIA module, the sinusoidal excitation current serves as the reference signal, which is correlated with the battery’s response voltage. Since impedance data is often used to estimate battery temperature, the test conditions were set to include excitation frequencies from 1 to 100 Hz, sampling rates between 250 and 1500 Hz, and signal-to-noise ratios ranging from 10 to 60 dB. This setup allows us to evaluate the accuracy of impedance calculations under various conditions.
Figure 2: Simulink model of DLIA-based impedance measurement system
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