# A New Calibration Method for Broadband Complex Resistivity Measurement System of Rocks and Ores
## 5 Results  
In this section, multiple circuit models were designed for testing, comparing the measurement accuracy of our instrument with the Solartron 1260A impedance analyzer. Combined with the test results from rock and ore samples as well as NaCl solutions, we analyzed the overall stability and accuracy of the measurement system, further validating the effectiveness of the calibration algorithm. First, we tested the impedance values of pure resistances of 1 k\(\Omega\) and 1 M\(\Omega\) (Figure 13), comparing them with the results from the Solartron 1260A impedance analyzer. For the low resistance test, the results from both instruments were similar, with a high-frequency phase shift of approximately 0.5 mrad, and both the resistance and phase curves were relatively smooth, indicating good instrument stability. However, the results from the two instruments showed significant discrepancies in the tests involving more extensive, more significant sampling resistances. Our instrument exhibited a more petite polarization shift at high frequencies than the Solartron 1260A. The internal parasitic capacitance of the tested 1 M\(\Omega\) resistor was determined to be approximately 0.50 pF, with a theoretical phase shift of around 300 mrad, which aligns closely with our instrument's measurements. Table 2 presents the test results for two instruments across a resistance range of 100 \(\Omega\) to 10 M\(\Omega\), using test resistors with a precision of 0.5% and parasitic capacitance below 1 pF. The complex resistivity data was converted into resistance and capacitance parameters for comparison. The results reveal that as the test resistance increases, the measurement accuracy of the proposed instrument (CSUZA-FW08) progressively surpasses that of the Solartron 1260A impedance analyzer. The resistance error of the CSUZA-FW08 consistently remains within 1%, while the capacitance measurements stay below 1 pF, accurately reflecting the actual characteristics of the test resistors. More significant errors observed at high frequencies with the Solartron 1260A impedance analyzer can be attributed to its input impedance (300 M\(\Omega\)), much lower than that of our instrument (17 G\(\Omega\)). Additionally, the small sampling resistance used resulted in decreased measurement accuracy when testing high-impedance samples. Our instrument achieves precise measurements of high-impedance samples by increasing the sampling resistance and employing an adaptive matching calibration algorithm. It is also evident that the internal parasitic capacitance of the 1 M\(\Omega\) pure resistor can cause a phase shift of around 300 mrad at high frequencies. Therefore, considering the influence of the sampling resistance's parasitic capacitance in the calibration model can further enhance the accuracy of the calibration algorithm. Figure 12: Complex resistivity testing results of the limestone sample before and after calibration. Figure 14 compares the complex resistivity test results between our instrument and the Solartron 1260A impedance analyzer, both using the sample holder shown in Figure 10a for measurement. The tested sample was lead-zinc ore. The results from the complex resistivity tests indicate that this sample exhibits low resistance and high polarization characteristics, with the resistivity magnitude decreasing with increasing frequency. The phase curve characterizes the sample's double-layer polarization at low frequencies and interface polarization effects at high frequencies. The results from both instruments are similar, with smooth testing curves, indicating high stability and accuracy of the measurement system, along with strong anti-interference capability. We also tested solution samples using the instrument shown in Figure 10b. Figure 15 compares the phase test results for NaCl solutions of different resistivities with their theoretical calculations.