## 1 Introduction
To avoid the injection locking phenomenon, they used a Phase-Locked Loop (PLL) structure, which ensured that the OEO operated under quasi-locked conditions. The RF signal detected in their work provided a maximum gain of 59.49 dB and a detection sensitivity of \(-\)120 dBm [12]. [PERSON] et al. (2023) generated a 1550/1560 nm two-color electro-optical frequency comb by modulating two continuous-wave lasers using a common electro-optical modulator and phase-locking their beat frequencies. They effectively suppressed the phase noise of the frequency comb modes accumulated from the RF synthesizer [13]. [PERSON] et al. introduced a 25.8 GHz integer-N Charge Pump Phase-Locked Loop (CPPLL) that demonstrates strong locking performance. The proposed Time-Amplified Phase-Frequency Detector (TAPFD) greatly suppresses in-band noise through phase error amplification gain [14]. This paper investigates the structural optimization, signal detection, and extraction difficulties of coil sensor probes in CFRP eddy current non-destructive testing (NDT) systems. The '8' type structure probe was improved by adopting an '8' type structure planar coil probe sensor, which is more sensitive to electric signals for signal acquisition. The study delves into the composition of lock-in amplifiers based on the principle of phase-locked amplification. A dual-phase-sensitive lock-in amplifier circuit was developed to overcome the difficulty of single lock-in amplifiers that require accurate phase adjustment. The circuit was verified through simulation experiments. The magnetic field distribution of a circular planar coil can be viewed as a superposition of the magnetic fields generated by concentric current rings of different diameters. Figure 2 shows the spatial magnetic field distribution for a single current ring. In the figure, the XYZ coordinate system is constructed with the center of the coil as the origin, and \(R\) represents the polar coordinates of any point P in the radius space of a single current loop as (\(\theta\),\(r\),\(z\)). A multiturn planar helical coil can be approximated as a superposition of concentric rings with different radii. The magnetic field distribution of a multi-turn coil can be obtained. At the center of the nth-turn coil, denoted by point P, the magnetic field strength is given by Equation (2):  
\[H_{N}(z)=\sum_{n=1}^{N}\frac{IR_{n}^{2}}{2{(R_{n}^{2}+d^{2})}^{3/2}} \tag{2}\]  
where \(d\) is the distance from point P to the center of the coil, which can be calculated quite simply using the polar formula; \(R_{n}\) is the radius of the nth-turn coil. However, due to the limitation of the structure's size, the small inductance and large resistance of the sensor make signal acquisition and detection difficult. Therefore, in this paper, we used frequency-specific filtering of the output signal to obtain an effective signal [18], and a lock-in amplifier [19] realized by using the frequency-transformed heterodyne technique to significantly improve the \(Q\) value. Based on the above principles, this paper developed a new phase-locked amplifier circuit suitable for detecting the signals of planar coil probe sensors for low-conductivity carbon fiber-reinforced resin materials, and conducted in-depth theoretical analysis and simulation experimental research on it.