# A New Calibration Method for Broadband Complex Resistivity Measurement System of Rocks and Ores
## 2 Measurement System  
### System Overview  
The calibration work in this study was conducted using a self-developed broadband electrical property measurement instrument for rocks andores (CSUZA-FW08). Figure 1 presents the structural diagram of the measurement system. The instrument consists primarily of the execution unit, the measurement apparatus (sample holder), and an Android App. The measurements are performed using the four-electrode method, with a test frequency range covering one mHz to 100 kHz. The central unit of the instrument, the execution unit, is the core of the measurement system. It consists of three main components: the signal source, acquisition system, and control system. The primary function of the execution unit is to receive control commands from the Android app, provide an integrated excitation source, perform core data acquisition, and transmit the data. The low-power control system is based on an embedded control board equipped with Bluetooth and WiFi modules. These modules connect the Android app to the data acquisition board. The control board receives configuration and acquisition commands from the app, which are then parsed and forwarded to the acquisition board. The control board also processes the data collected by the acquisition board and uploads it to the Android app after packaging. The signal source uses a board-level signal generator that provides sinusoidal signals at different frequency settings. It offers multiple adjustment levels to achieve five constant voltage outputs (1 mV, 10 mV, 100 mV, 1 V, and 10 V) and five constant current outputs (1 \(\mu\)A, 10 \(\mu\)A, 100 \(\mu\)A, 1 mA, and 10 mA). The signal frequency accuracy reaches 0.1 ppm, ensuring distortion-free excitation of the samples. The high-precision acquisition system is designed with four acquisition channels. The core component of the system is the FPGA model XC7K325T-2 FFG900I. This system uses ultra-high input impedance (>1 G\(\Omega\)) technology to reduce channel leakage currents. The voltage and current resolutions are 1 \(\mu\)V and 1 nA, respectively. Additionally, the instrument is equipped with an adaptive sampling resistor network, extending the resistance range to 50 \(\Omega\)-10 M\(\Omega\). During testing, the system can automatically match the sampling resistor to the actual impedance of the sample, accommodating the measurement requirements of high-impedance rock and ore samples. The Android app, serving as the control software, is responsible for sending configuration and control commands, as well as receiving and storing data. It also includes impedance calculation and data calibration algorithms for real-time graphical data display, enabling users to easily control and monitor the system. Data communication between the app and the embedded control board is facilitated through Bluetooth and WiFi protocols, with Bluetooth handling control commands and WiFi managing real-time data transmission. To meet the testing requirements of different samples, we designed two sets of sample holders. These sample holders are connected to the instrument using BNC triple-coaxial shielded cables, eliminating errors caused by electromagnetic coupling in the four-electrode method. Figure 1: Structural diagram of the broadband rock and ore electrical measurement system. The signal source generates a highly stable driving signal via a direct digital synthesizer (DDS) and a constant current/voltage module, which is further adapted to diverse measurement requirements through a multi-range adjustment module. During the measurement process, the voltage difference (\(\Delta U_{\text{Im}}\)) across the two ends of the sample holder is detected. The signal is subsequently filtered through a low-pass filter (LPF) before being digitized by an analog-to-digital converter (ADC) and analyzed by a field-programmable gate array (FPGA) for data processing and logical control.