## 1 Introduction  
Carbon Fiber-Reinforced Plastics (CFRP) are composite materials composed of carbon fibers and a resin matrix. Compared to metal materials, carbon fiber composites have many advantages. They have low density and high strength [1]. In comparison to conventional steel, their service life is extended by 2-3 times, and their tensile strength can reach up to 3500 MPa, which is five times that of steel [2]. Carbon fiber has several advantages, including a small coefficient of thermal expansion, good thermal conductivity, high and low temperature resistance, and good resistance to sudden changes in temperature [3]. Due to these excellent characteristics, it is widely used in high-precision technology fields such as aerospace, ocean-going ships, rail transportation, and new energy vehicles [4]. Although CFRP have excellent properties, defects may occur during production or due to external environmental factors. The complexity of CFRP processing and factorssuch as low molecular impurities in the prepreg, solvents, and moisture volatilization can contribute to the formation of these defects [5]. These defects, such as voids, cracks, and delaminations, can significantly reduce the serviceability of the component and shorten its life. The development of nondestructive testing technology for CFRP materials is significant. Some scholars have improved the sensitivity of the inspection coil by designing specific coil structures. [PERSON] et al. analyzed the impedance of rectangular planar coils and bending-type coils through finite element numerical analysis and compared the results with experimental data to reveal the influence of different coil parameters on impedance [6]. [PERSON] proposed a circular array sensor including 16 coils [7]; this method effectively reduces noise due to mechanical rotation and is able to efficiently capture the texture characteristics of the fibers. [PERSON] experimentally used a pair of 45\({}^{\circ}\) parallelogram coils on CFRP with low conductivity in tests; minimal side cuts and fiber breaks were detected, and the experiments showed a good signal-to-noise ratio [8]. For the detection of curved pipes with natural concave defects, [PERSON], [PERSON], proposed a transmit-receive Flexible Printed Coil (FPC) array using the Wireless Power Transfer (WPT) method for a material surface using the WPT principle. The single excitation coil and multiple receiving coils of the material surface were experimentally investigated for mapping and reconstruction of defective depressions for quantitative nondestructive inspection through feature selection and feature fusion by deep learning [9]. [PERSON] et al. fabricated a rectangular planar inductive coil with a wire diameter as small as 10 \(\upmu\)m. They then simulated and analyzed the magnetic field around the coil using FEM software (ANSYS(r) version 12.1). The coil was successfully used to capture and manipulate magnetic particles [10]. When a magnetic sensor measures a magnetic field, the signal strength at the receiving end may vary due to changes in the distance between the probe and the test sample, leading to uncertain results. To address this issue, [PERSON] and colleagues developed a specialized probe that features an '8'-shaped transmitting coil and a circular receiving coil. This probe is highly sensitive in detecting defects and is not affected by changes in lift-off distance [11]. This signal is often submerged in a larger background signal composed of the ambient magnetic field and circuit noise. The detection and extraction of a weak magnetic field signal is a crucial part of nondestructive CFRP testing technology. In addition to the probe structure and lift-off effect mentioned above, one way to solve this problem is through the use of a phase-locked loop. [PERSON] et al. proposed a scheme for detecting weak Radio Frequency (RF) signals based on a single-mode Opto-Electronic Oscillator (OEO).