# Absolute Capacitance Measurement by Direct Digital Fitting of Proportional Coefficient
## 1 Introduction
[23], in a discussion of electrical capacitance tomography (ECT) principles, introduced ECT systems based on charge-discharge capacitance measurement circuits, which have been used for visualization of oil pipelines. Realizing wide-range capacitance absolute measurements is a challenging task. Many traditional measurement methods are often limited to narrow measurement ranges, making it difficult to meet diverse industrial needs. In order to overcome this challenge, a capacitance absolute measurement method based on direct fitting of proportional coefficient is proposed here for the voltage source method, where the input and output signals are sampled and converted to digital quantities by Analog-to-Digital Converter (ADC), and the proportional coefficient is solved by direct fitting according to the property that the difference between the square wave input signal and the analog voltage output signal with RC RC time constant is proportional to the slope of the analog voltage output signal with RC time constant function in a first-order RC system. The relationship between the proportional coefficient and the capacitance to be measured is then utilized to perform capacitance tolerance calculations when the reference resistance is known. Compared to the standard charge-discharge method, the approach proposed in this paper does not require waiting for the completion of capacitor charging or discharging, nor does it impose constraints on the duration of these processes. Instead, it calculates the capacitance solely based on the sampled input and output signal data. The triggering conditions are significantly simpler. In traditional charge-discharge methods, each cycle must charge or discharge to at least half of the input voltage, and the starting voltage must be either 0 or the full voltage. The method presented in this paper achieves a wide measurement range while maintaining high precision. Additionally, this method exhibits strong noise suppression capabilities, providing stable and reliable results. Furthermore, it imposes lower requirements on hardware performance, eliminating the need for excessively high analog-to-digital conversion accuracy, resolution, or speed. This means that efficient and cost-effective absolute capacitance measurement can be achieved without demanding extreme hardware specifications. This capacitance measurement method, leveraging its high stability and wide measurement range, could be applied to various capacitance sensing measurements in the future. Applications include: soil moisture monitoring in environmental monitoring by measuring capacitance variations under different humidity levels; biomedical sensors (which often rely on capacitance changes to detect physiological parameters) could see enhanced precision in medical devices through expanded measurement ranges; supercapacitors (widely used in energy storage systems with typically large capacitance values) may benefit from improved performance evaluation and management systems via enhanced measurement techniques. Additionally, the method could analyze dielectric properties of new materials, accelerating the development of advanced materials such as high-performance dielectric materials for electronic devices or energy storage systems. Overall, compared to other traditional methods, the proposed approach offers a broader measurement range, simpler circuit design, more lenient triggering conditions, lower cost, and stronger anti-interference capabilities. It is more suitable for various capacitance measurement applications.