# A New Calibration Method for Broadband Complex Resistivity Measurement System of Rocks and Ores
## 3 Analysis and Calibration of the Instrument's Acquisition Circuit
### Reverse Connection of the Signal Source
By calculating the actual impedances \(Z_{\text{s}}\) of different sampling resistances and the measured values \(Z_{\text{m2}}\) for the reverse connection configuration using standard components, this information can be integrated into the data acquisition program to enable automatic data calibration for varying sample impedances under the forward connection configuration. It is important to note that the forward and reverse connection testing method does not require two measurements for each sample, as this would significantly reduce acquisition efficiency. During normal testing, the forward connection configuration of the signal source is still employed, while the reverse connection configuration functions similarly to the calibration process. Calibration data for different sampling resistances can be established once, and the capability to switch between forward and reverse connections can be integrated into the App control interface for user convenience. To further validate the accuracy of the analytical results, a low-resistance testing model with a pure resistance of 1 k\(\Omega\) was designed. Adaptive testing of the sampling resistance (also set at 1 k\(\Omega\)) was conducted under both the signal source's forward and reverse connection configurations. The test results before calibration are shown in Figure 4:2 The phase curves for the forward and reverse connections satisfy \(\varphi_{\text{m1}}=-\varphi_{\text{m2}}\), and the resistance magnitudes \(Z_{\text{m1}}\times Z_{\text{m2}}={R_{\text{s}}}^{2}\), consistent with the characteristics outlined in Equation (20). Conventional data calibration methods generally utilize the forward connection of the signal source, with calibration performed using Equation (11). To reduce the influence of the sampling resistor on calibration accuracy, sampling resistors with values below 1 k\(\Omega\) are commonly selected. In this study, a forward-reverse switching approach for the signal source connection is adopted. Initially, the reverse connection is employed to calibrate sampling resistors with a wide range of resistances (50 \(\Omega\)-10 M\(\Omega\)). The forward connection is then used to obtain the raw complex resistivity data of rock samples prior to calibration. Finally, the data is calibrated using Equation (20). This method offers the advantage of eliminating the restriction to low-value sampling resistors (below 1 k\(\Omega\)) by calibrating the parasitic capacitance of large sampling resistors, thereby enabling high-precision measurements for high-impedance samples. To evaluate the method, a 10 k\(\Omega\) pure resistor model was tested and calibrated using both the traditional forward connection method and the proposed forward-reverse switching  
Figure 4:3 Impedance test results for a 1 k\(\Omega\) resistor using forward and reverse connection methods of the signal source, showing uncalibrated data. method, as shown in Figure 4:4 The results indicate that the proposed method achieves superior resistance accuracy. While phase deviations were observed at high frequencies, measurements conducted using an LCR bridge instrument revealed that the parasitic capacitance of the 10 k\(\Omega\) resistor is approximately 0.46 pF, with the theoretical phase at 100 kHz being about 2.9 mrad, closely matching the calibration results. Figure 8 presents the test results for three sets of parallel resistor-capacitor models. The product of resistance \(R\) and capacitance \(C\) for each model is kept consistent, with varying values employed to assess whether the instrument can achieve the same accuracy under different sampling resistances. The resistance and capacitance values for the three sets of models are detailed in Figure 4:5 The testing results show that the precision of the first two sets is within 1%, showing good agreement with the theoretical curves. However, the phase curve of the third set exhibits slight deviations from the theoretical values.