# Current-Sensing Topology with Multi Resistors in Parallel and Its Protection Circuit
## 3 Results
### Time Delay Property of Protection Circuit
To eliminate the hiccup issue in protection circuits, it is necessary to make \(t_{1}<t_{2}\). In the experimental circuit, the gains were \(G_{1}=800/3\) and \(G_{2}=24\). It can be calculated that \({I_{T1}}\) = 4.5 A and \({I_{T2}}\) = 5 A. The hysteresis ratios of comparison circuits 1 and 2 were 11% and 19.6%, respectively. One can calculate that \({I_{T1-}}\) = 4.005 A, \({I_{T1+}}\) = 4.995 A, \({I_{T2-}}\) = 4.02 A, \({I_{T2+}}\) = 5.98 A. When \({I_{IN}}\) = 6 A, it could be measured via the cursor function of the power analyzer that \({I_{R2}}\) = 0.93 A and \({I_{R1}}\) = 5.07 A, as shown in Figure 16a. In protection circuit 1, let the resistance and capacitance of the first-order low-pass filter be 100 k\(\Omega\) and 1 uF, respectively. That is, \(\tau_{1}\) = 100 ms. By setting \(t_{1}=t_{2}\), the critical point for eliminating hiccups can be calculated as \(\tau_{2}\) = 850 ms, according to Equations (54) and (55). To meet \(t_{1}<t_{2}\), one should make \(\tau_{2}\) > 850 ms. The test waveforms are shown in Figure 14:3  
In Figure 16a, the current acquired via the power analyzer repeatedly switches between 6 A and 0.93 A, indicating the occurrence of protection hiccups. From Figure 16d-f, the red and blue waveforms were rectified mean output \(V_{RM1}\) and \(V_{RM2}\) for circuit 1 and 2, respectively. In Figure 16d, during the process of \(V_{RM2}\) decreasing from the positive comparison threshold of 2.88 V to the negative threshold of 1.92 V, there was no time for \(V_{RM1}\) to rise to the positive comparison threshold of 2.664 V, resulting in protection hiccups. In Figure 16e, as \(\tau_{2}\) increased, \(V_{RM1}\) rose higher, but was still lower than 2.664 V. The hiccup still existed, as shown in Figure 16b. In Figure 16f, \(\tau_{2}=880\) ms > 850 ms, the protection hiccup was eliminated, as shown in Figure 16c. It should be mentioned that two different time scales are used in Figure 14:4 In Figure 16a,d, the time scale is 200 ms/div; in Figure 16b,c,e,f, the time scale is 1 s/div. From the above analysis and tests, it can be concluded that the following conditions should be met to eliminate the protection hiccup:  
1. The protection thresholds were set as \({I_{T1+}}^{\prime}<{I_{T2+}}\);
2. \(\tau_{2}\) was significantly higher than \(\tau_{1}\);
3. Comparison circuit 2 had a high hysteresis ratio. The above test is based on DC input current. What is the difference if the input is an AC waveform? According to Equations (31)-(33), all outputs of the rectified mean circuits for these three waveforms can be expressed as the combination of first-order step response of rectified mean value and AC ripple. When \(\Omega\geq 10\), the ripple amplitude is much lower than the rectified mean value. The delay issue caused by first-order filters is similar to that of the DC input, with time constants of \(\tau_{1}\) and \(\tau_{2}\). The conditions for eliminating protection hiccups are the same as for DC input. AC ripple may cause further protection hiccup issues. The hysteresis ratios of comparison circuits need to be considered according to it. According to Equation (46), while \(\Omega\geq 10\), the ripple ratio is at a maximum at \(\Omega=10\). The ripple ratios for various waveforms are shown in Figure 14:5  
Figure 14:6 Measured waveforms: Current waveforms while (**a**) \(\tau_{2}=100\) ms; (**b**) \(\tau_{2}=680\) ms; (**c**) \(\tau_{2}=880\) ms. Output waveforms of rectified mean circuits while (**d**) \(\tau_{2}=100\) ms; (**e**) \(\tau_{2}=680\) ms; (**f**) \(\tau_{2}=880\) ms.  
From Table 4, it can be concluded that as the duty cycle decreases, the ripple ratio for periodic pulse input increases. According to Table 2, the parallel overcurrent protection based on rectified mean detection is more effective while \(D\geq 1/3\). When \(D<1/3\), peak detection based on ADC sample values takes over the role. In summary, for a protection circuit based on rectified mean detection, the highest ripple ratio is 10.4%, while the input is periodic pulse wave and \(D=1/3\).