# Current-Sensing Topology with Multi Resistors in Parallel and Its Protection Circuit
## 2 Materials and Methods
### Parallel or Series Multi Resistor Current-Sensing Topology
#### 2.1.2 Current-Sensing Topology with Multi Resistors in Parallel  
When multi sensing resistors are connected in parallel, the current flows only through the selected switch and sensing resistor. Figure 3 shows the case with two resistors. In Figure 3, if the value of the sensing resistor is low, a four-wire resistor should still be used. The corresponding gain circuit \(G_{1}\) or \(G_{2}\) needs to be a differential amplification circuit. \(R_{2}\) has higher resistance value, covering lower ranges, while \(R_{1}\) has lower value, covering higher ranges. When a user selects lower ranges, the switch \(S_{2}\) is closed and \(S_{1}\) is open. The input current flows through \(S_{2}\) and \(R_{2}\). Voltage \(V_{\text{O2}}\) is selected. When switching to higher ranges, the switch \(S_{1}\) is closed and \(S_{2}\) is open. Voltage \(V_{\text{O1}}\) is selected. \(D_{1}\) and \(D_{2}\) are bi-direction freewheeling diodes. They provide current paths for moments when both \(S_{1}\) and \(S_{2}\) are open. In the parallel sensing circuit, the freewheeling diodes are shared by all sensing resistors, so there is a lower component count compared to the series counterpart. On the other hand, when there are more sensing resistors \(R_{3}\), \(R_{4}\),...and more switches \(K_{3}\), \(K_{4}\),..., each switch only needs to be capable of conducting a current within the corresponding ranges. Only \(S_{1}\) is conducting when the highest range is selected. Compared with all switches conducting in a series circuit in this case, the parallel sensing circuit has significant advantages in terms of layout space and heat dissipation. In Figure 3, the sensing resistor is connected in series with the switch. If the selected switch is switched off for overcurrent protection, the current would flow through diodes \(D_{1}\) and \(D_{2}\). The forward voltage of diodes is considerably higher than the voltage drop of the original sensing path. For high input current, the power consumption of diodes would be too high to be dissipated. Therefore, the higher range's sensing path should be switched on for overcurrent protection. This works as in following steps:  
1. The initial condition: A lower range is selected and \(S_{2}\) is closed. Let the maximum allowed current of sensing resistor \(R_{2}\) be \(I_{\text{T2}}\). When the sensed current \(I_{R2}>I_{\text{T2}}\), the switch \(S_{1}\) is forced to close. 2. Then, the current is divided into both resistors \(R_{1}\) and \(R_{2}\). The current values are calculated by Equations (4) and (5) respectively, where \(R_{S1}\) and \(R_{S2}\) are the conduction resistance of \(S_{1}\) and \(S_{2}\). Since \(R_{S1}+R_{1}\) is generally 1/10\(\sim\)1/4 times \(R_{S2}+R_{2}\), most of the current is diverted to the sensing path of \(S_{1}\) and \(R_{1}\) to prevent the damage of \(S_{2}\) and \(R_{2}\) due to overheating. \[I_{R1}=I_{IN}\times(R_{S2}+R_{2})/(R_{S2}+R_{2}+R_{S1}+R_{1}) \tag{4}\]  
Figure 3: Two resistors in parallel current-sensing topology. \[I_{R2}=I_{IN}\times(R_{S1}+R_{1})/(R_{S2}+R_{2}+R_{S1}+R_{1}) \tag{5}\]  
When the above protection mechanism is adopted, the protection hiccup would occur as follows:  
1. While \(S_{1}\) is closed, the current sensed by \(R_{2}\) is decreased to \(I_{R2}\) = (1/11\(\sim\)1/5) \(\times\)\(I_{IN}\). In most cases, \(I_{R2}\) is now lower than \(I_{T2}\). The overcurrent condition is not met any more. The switch \(S_{1}\) returns to open. 2. After \(S_{1}\) is open, \(I_{R2}=I_{IN}>I_{T2}\). The protection will be triggered again to make \(S_{1}\) closed. 3. The above two steps occur alternately. This is called protection hiccup. A protection hiccup appears because the overcurrent state could not be latched. To improve this, a protection circuit with dual threshold detection is designed, as shown in Figure 4.  
In Figure 4, \(S_{1}\) is closed at a high level of control input and vice versa. \(CTR_{1}\) is the switch control signal from the module controller.