# Absolute Capacitance Measurement by Direct Digital Fitting of Proportional Coefficient
## 5 Conclusions  
In this paper, for the measurement of capacitance, a method based on the direct fitting of proportionality coefficients is realized, and a method is proposed in which the difference of the response curve is proportional to the difference between the input and the output, and the size of the capacitance can be calculated as long as the proportionality coefficients are calculated by fitting. Leveraging the 12-bit DAC and ADC integrated within the STM32, the generation of square wave excitation signals and the synchronous acquisition of square wave response signals are achieved. Under conditions of continuous square wave response and a sampling frequency of 560 kHz, the method is tested to meet the requirements for high-accuracy measurement of capacitance values ranging from 60 pF to 60 nF. This method offers a practical solution for wide-range capacitance measurement. This capacitance measurement method is not affected by the initial voltage conditions of the capacitance being measured, which effectively avoids the influence of voltage and current noise at the start and end points of the measurement, thereby improving the accuracy and stability of the measurement. This method is advantageous for the absolute measurement of capacitance because it meets the need for wide-range measurements and reduces system complexity and cost while maintaining high accuracy. This approach provides a different way of thinking for applications that require a large range of capacitance measurements.  
Conceptualization, X.W. and Q.S.; methodology, X.W.; software, X.W.; validation, X.W., Q.S. and S.C.; formal analysis, Q.S.; investigation, Q.S.; resources, X.W., D.L. and B.X.; data curation, Q.S. and J.L.; writing--original draft preparation, Q.S.; writing--review and editing, D.L.; visualization, Q.S.; supervision, P.L.; project administration, X.W.; funding acquisition, X.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Hubei Provincial Innovation Group Program, grant number 2022 CFA006.  
Not applicable.  
The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.  
\begin{table}
\begin{tabular}{c c c c} \hline
**References** & **Measurement Methods** & **Measurement Range** & **Measurement Deviation** \\ \hline
[28] & A.B./Active De-Sauty & 900 pF–1.1 nF & \textless{}10\% \\
[29] & Modified De-Sauty AC Bridge. & 100 pF–2 nF & \textless{}6\% \\
[30] & Active bridge + relaxation oscillator & 1 pF–619 pF & \textless{}2.33\% \\
[31] & Dual-slope + PSD & 66 pF–506 pF & \textless{}1\% \\
[32] & Capacitance to relaxation time & (1) 2 pF–10 pF & (1) \textless{}8\% \\  & Charge–discharge method & (2) 100 pF–1 nF & (2) \textless{}1\% \\ This work & Proportionality coefficients are & (1) 60 pF–800 pF & (1) \textless{}0.9\% \\  & directly fitted & (2) 800 pF–60 nF & (2) \textless{}0.2\% \\ \hline \end{tabular}
\end{table}
Table 6: Performance comparison of different measurement methods.