Lithium-ion battery internal resistance and impedance are among the most critical parameters that determine battery performance, lifespan, and operational condition. These characteristics provide essential insights into how easily electrons and ions move within the electrode materials. Accurate impedance measurement plays a vital role in the development, manufacturing, and application of batteries. During operation, changes in impedance can indicate the battery's health status, allowing for early prediction of its remaining life. Additionally, by analyzing the impedance angle and mode, it is possible to estimate the internal temperature of the battery. Therefore, precise measurement of internal resistance is an essential requirement for battery management systems and real-world applications.
Common methods for measuring battery impedance include:
1. Determining the impedance mode using the amplitude of the response voltage and excitation current, and calculating the time difference between them 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 especially phase measurements, making it unsuitable for high-precision impedance calculations.
3. Correlation-based calculation methods. Due to the small internal resistance of batteries, noise and interference significantly affect measurement accuracy. A digital lock-in amplifier (DLIA) uses correlation detection to suppress noise, enhance signal-to-noise ratio, maintain stable center frequency, narrow bandwidth, and improve signal extraction capabilities.
In this paper, 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 Impedance Measurement Using a Digital Lock-In Amplifier**
**1.1 Algorithm Design**
The response voltage of a battery 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 the core component of internal resistance measurement. It operates based on correlation detection, where the reference signal frequency is correlated with the input signal frequency, while non-synchronous noise is not. This enables the extraction of useful signals from noisy environments. Based on the fundamental principle of lock-in amplifiers, we propose directly using the current signal as the in-phase reference, obtaining the quadrature reference signal through an orthogonal algorithm, and then calculating the impedance. The measurement principle of battery impedance is illustrated in Figure 1.
Figure 1: Impedance measurement principle
**1.2 Simulink Simulation Verification Based on DLIA Impedance Measurement**
To verify that the digital lock-in amplifier can effectively suppress noise and interference in internal resistance measurements, improving measurement accuracy, we built the model shown in Figure 2 in Simulink. The ExcitationSource module generates a sinusoidal excitation current to stimulate the battery, while the battery module uses a commonly used second-order RC equivalent circuit model. In the DLIA module, the sinusoidal excitation current is used directly as the reference signal to correlate with the battery’s response voltage. In practical applications, battery impedance information is often used to estimate internal temperature. Therefore, the test conditions were set to: excitation frequencies ranging from 1 to 100 Hz, sampling frequencies from 250 to 1500 Hz, and signal-to-noise ratios from 10 to 60 dB. This setup allows us to evaluate the accuracy of impedance calculations under various excitation frequencies and signal-to-noise ratios.
Figure 2: Simulink model of the DLIA-based impedance measurement system
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