## 4 Conclusions  
In this study, we designed a compact and highly sensitive long-wave broadband direction-finding system. The system uses two magnetic antennas and one electric antenna, operating over a bandwidth of 10 kHz to 300 kHz. The diameter of the receiving equipment is limited to 45 cm, while maintaining exceptionally high sensitivity. Furthermore, both the magnetic and electric field sensors exhibit flat sensitivity across the device's operating bandwidth, a feature not found in other devices in existing research. The flat sensitivity across a wide bandwidth ensures that broadband signal waveforms, such as lightning pulses, remain undistorted upon reception, facilitating a more accurate study of their characteristics.  
The miniaturization of the equipment enables adaptation to a wider range of application scenarios with minimal site requirements. For direction finding, the system primarily  
Figure 17: Phase analysis of signals from main and reference receivers within five seconds in the JJI (22.2 kHz) signal bandwidth.  
Figure 18: Phase analysis of signals from main and reference receivers within five seconds in the JJY60 (60.0 kHz) signal bandwidth.  
relies on magnetic antennas, supplemented by electric antennas. The use of multiple antennas ensures accurate direction finding of global long-wave radios in various electromagnetic environments, maintaining a maximum direction finding error of less than 2\({}^{\circ}\) across a range of angles from 9.9\({}^{\circ}\) to 170.1\({}^{\circ}\).  
This paper also analyzes the signal characteristics of two modulation modes commonly used in long-wave radios and proposes distinct direction-finding algorithms based on the characteristics of these modulation signals, which have not been discussed in previous studies and provide theoretical support for subsequent long-wave radio direction finding and positioning. The device can serve not only as a precise positioning tool for mobile platforms when GPS is unavailable, but also has potential applications in detecting and localizing lightning pulses and diagnosing ionospheric D-regions.  
However, the miniaturization of the device results in a slight reduction in sensitivity, particularly when compared to larger antennas, making it unable to detect extremely weak or distant signals. Future research should focus on optimizing sensor sensitivity, such as by refining the amplifier circuit design for the electrical sensors to achieve a lower noise level.  
Conceptualization, H.L. and S.W.; methodology, H.L.; software, H.L.; validation, H.L., S.W., and X.X.; formal analysis, H.L. and X.X.; investigation, H.L. and S.W.; resources, S.W.; data curation, Y.J.; writing--original draft preparation, H.L.; writing--review and editing, X.X., Y.J., and S.W.; visualization, H.L.; supervision, X.L.; project administration, X.L.; funding acquisition, X.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} MSK & Minimum Shift Keying \\ ASK & Amplitude Shift Keying \\ ELF & Extremely Low Frequency \\ VLF & Very Low Frequency \\ LF & Low Frequency \\ GPS & Global Positioning System \\ ADC & Analog-to-Digital Converter \\ SNR & Signal-to-Noise Ratio \\ TR Noise & Thermal Noise of the Coil Resistor \\ CV Noise & Circuit Equivalent Input Voltage Noise \\ CI Noise & Circuit Equivalent Input Current Noise \\ PPS & Pulse Per Second \\ \end{tabular}