# A New Calibration Method for Broadband Complex Resistivity Measurement System of Rocks and Ores
## 4 Design and Calibration of the Measurement Instrument
During the design process of the sample holder using the four-electrode method, the electromagnetic coupling between the measurement electrodes and measurement lines is the primary concern, particularly affecting measurements at frequencies above 1 kHz and increasing with frequency. Therefore, BNC triple coaxial shielded cables were selected to connect the measurement device to the equipment. The sample holder is made of polymer materials, providing excellent electrical insulation and chemical corrosion resistance. Furthermore, the current electrodes (power electrodes) and voltage electrodes (measurement electrodes) are made from copper alloy, with an area of 10 cm \(\times\) 10 cm. This ensures good oxidation resistance to effectively mitigate the impact of low-frequency electrode polarization on data results. This also facilitates uniform current flow through the sample. A saturated CuSO\({}_{4}\) solution is placed within the sample holder container to minimize electrochemical reactions with the electrodes. Additionally, the CuSO\({}_{4}\) electrolyte technology solution reduces the electrolyte's resistivity to a minimum (with resistivity less than 0.1 \(\Omega\cdot\)m), allowing \(Z_{1}\) and \(Z_{4}\) to drop below 1 \(\Omega\), making their impact on the measurement results negligible. Data calibration can be performed using Equation (20). The sample holder is designed for convenience and ease of operation and is secured by a support frame to ensure sample stability during testing. A copper sulfate paste contacts the voltage electrode and the sample, reducing contact impedance. To prevent creeping currents on the rock's surface and evaporation of moisture during testing, plastic wrap can cover the sides of the rocks. Figure 10: Schematic diagrams of two measurement devices: (**a**) the diagram used for measuring standard rock samples such as ores, and (**b**) the device employed for testing solutions and loose samples. The device shown in Figure 10b meets the corresponding requirements for testing sand and liquids. This design can also be divided into four parts: A for the power electrodes; B for the measurement electrodes; C for the base; and D for the sample container. Acrylic glass is chosen as the design material for this sample holder. To minimize the impact of power electrode polarization on the measurement electrode, the distance between the two should be approximately twice the sample spacing (i.e., the spacing between the measurement electrodes) [27]. The power electrodes remain made of copper alloy, but the measurement electrodes are altered. For rock samples testing, planar electrodes are selected to maximize the contact area with the sample, thereby reducing transition resistance. In contrast, point-type AgCl electrodes are used for water or sand tests to minimize errors caused by poor coupling between the electrode and sample [4]. The AgCl electrodes exhibit strong electrochemical stability and minimal polarization effects. In this case, the stray impedances \(Z_{1}\) and \(Z_{4}\) between the power electrode and measurement electrode are primarily induced by the sample itself and cannot be neglected; therefore, calibration should be performed using Equation (23). To verify the calibration effectiveness of the measurement device, we designed a circuit model to simulate the polarization characteristics of samples and the device effects during actual rock sample testing, as shown in Figure 11. The figure presents a comparison between the calibrated test results and the theoretical results. It demonstrates a phase shift occurring between 1 Hz and 10 kHz, simulating the low-frequency double-layer polarization effects in rock and ore samples. After 10 kHz, the phase exhibits a downward trend again, simulating the high-frequency interface polarization effects. The calibrated test results show a high degree of consistency with the theoretical values, validating the accuracy of the calibration algorithm. Subsequently, we analyzed the testing performance of the sample holder shown in Figure 10a.