# A New Calibration Method for Broadband Complex Resistivity Measurement System of Rocks and Ores
## 6 Conclusions  
This study is based on the self-developed broadband rock and ore electrical measurement system, analyzing the errors generated within the instrument due to the distributed capacitance of the acquisition channel and the parasitic capacitance of the sampling resistor. By integrating two circuit design models (signal source direct connection and reverse connection), a new calibration method for the instrument is proposed. This method requires first measuring the spectral response characteristics of different sampling resistors with the signal source reversed and incorporating these as calibration values within the testing algorithm. Subsequently, the signal source direct connection method can be used to test samples of varying impedance values. The instrument's testing and calibration processes are fully controlled via a mobile App. Once calibrated, the App autonomously selects the appropriate sampling resistor based on the characteristics of the rock sample during measurement, performs data calibration, and displays the processed data in real time on the software interface, demonstrating strong practicality. The calibration method offers the following advantages:  
* **Simplicity**: It eliminates the need to consider the size of the instrument's internal acquisition channel distributed capacitance separately; calibration can be performed solely on the results from the direct and reverse connection tests. * **Detail**: The calibration content is refined, with the influence of the parasitic capacitance of the sampling resistor included in the equations, leading to a more comprehensive consideration. * **High Precision**: The adaptive testing method can achieve a testing accuracy of 0.1% for high-impedance samples (above 1 M\(\Omega\)), outperforming traditional small sampling resistor calibration methods. Based on the design of two measurement devices, the measurement errors caused by device effects were re-analyzed, leading to further improvements in the calibration algorithm. Through extensive testing with multiple circuit models and actual samples, the accuracy of the calibration method was verified, demonstrating good performance in practical applications. The resistivity accuracy achieved is 1%, with phase accuracy below 0.1 mrad at frequencies below 10 kHz, and phase accuracy controlled within 2 mrad between 10 kHz and 100 kHz. Comparative testing with the Solartrron 1260A impedance analyzer showed that the system and calibration method yield superior results for high-impedance samples. Additionally, tests with actual rock samples confirmed the effectiveness of the measurement system and calibration method in distinguishing mineralized samples, underscoring their significance for complex resistivity testing and rock physical property research. On the other hand, the accuracy of the calibration method decreases as the test frequency increases. This decline is partly due to the lack of precise measurement of the stray impedances \(Z_{1}\) and \(Z_{4}\) between the power supply electrode and the receiving electrode. Related scholars have already conducted in-depth studies by altering the circuit design [28]. Additionally, electromagnetic coupling between the four-point measurement system increases rapidly with frequency, and it cannot be completely eliminated. Currently, a combined two-point and four-point testing approach is used to measure the complex resistivity of samples up to MHz frequencies, thereby further extending the frequency range of sample measurements [2]. Conceptualization, R.C. and S.C.; methodology, R.C. ; software, H.Z. ; validation, H.Z. and C.X. ; formal analysis, H.Z. ; investigation, H.Z. ; resources, C.X. ; data acquisition and processing, H.Z. ; writing--original draft preparation, H.Z. ; writing--review and editing, R.C. and S.C.; supervision, R.C. ; project administration, S.C.; funding acquisition, R.C. and S.C. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Key R&D Program of China (Grant No.