# Current-Sensing Topology with Multi Resistors in Parallel and Its Protection Circuit
## 4 Discussion  
A new current-sensing method--multi resistors in parallel--was proposed in this article. The new method solved the problem of high heat consumption and large layout space occupation with bypass switches and freewheeling diodes in the series sensing method. The limit on the number of sensing resistors was broken through. Thereby, the dynamic range of a single current-measurement channel is improved. The overcurrent state cannot be latched in the parallel shunt protection circuit, resulting in protection hiccups. A dual threshold-detection circuit was proposed to solve the hiccup issue.  
In the protection circuit, rectified mean detection was used to roughly measure the effective value of the input current. Through analysis, it was found that the protection circuit based on rectified mean detection has good protection validity for sine, triangular and periodic pulse wave with duty cycle \(D\geq 1/3\). For periodic pulse wave with duty cycle \(D<1/3\), the validity is lower than the peak detection. Therefore, a protection scheme combining rectified mean-detection circuit and peak detection based on ADC sample values was proposed.  
Due to a delay in the rectified mean-detection circuit, if the time constant of the first-order filter and the hysteresis ratio of the comparison circuit are not properly set, protection hiccups may still appear. In order to obtain the dynamic response characteristics of the rectified mean-detection circuit for common waveforms, such as sine, triangular and periodic pulse waves, the following actions were taken: the absolutes of three waveforms were represented via Fourier series; their frequency domain expressions were then obtained through Fourier transform; after multiplying with the transfer function of the first-order filter, the time-domain expressions of three waveforms passed through the rectified mean circuit were obtained through inverse Fourier transform. All three waveforms can be expressed as the sum of the first-order step response and AC ripple. The first-order step response is similar to that of the DC input and the consideration on the time constant for eliminating the protection hiccup is the same; the AC ripple determines the hysteresis ratio of the comparison circuit. The calculation formulas for estimating the ripple ratio of three waveforms are provided in Equation (46).  
In the experimental circuit, 5 sensing resistors were used, covering 15 current ranges from 2.5 mA to 32 A. A total range ratio of \(1.28\times 10^{4}\) was achieved. This verified the  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Waveform** & **Duty Cycle** & **Ripple Ratio** \\ \hline Sine & / & 3.3\% \\ Triangular & / & 3.94\% \\ \hline Pulse & 0.9 & 1.57\% \\  & 0.7 & 4.7\% \\  & 0.5 & 7.83\% \\  & 1/3 & 10.4\% \\  & 0.3 & 11.0\% \\  & 0.1 & 14.1\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Ripple ratios of waveforms.  
superiority of multi resistors in the parallel sensing method in improving the measurement dynamic range. The correlation between parameters such as protection threshold, time constant of filter and hysteresis ratio and also the conditions for eliminating hiccups are given in Equations (54) and (55). The test results coincide with theoretical calculations.  
In addition to the power analyzer involved in this article, the current-sensing topology with multi resistors in parallel and the overcurrent protection method can be used in any current-sensing application with a large dynamic range requirement. The response characteristics of three common current waveforms as input were analyzed. However, the analysis method is universal and other waveforms can be analyzed through the process provided in the article.