## 2 Circuit Topology of RF-Energy-Harvesting Integrated Circuit
### Over-Voltage Protection Circuit  
Figure 4 presents an over-voltage protection circuit used to prevent the occurrence of a high-voltage breakdown phenomenon during NFC [19]. The output DC voltage Vdc of the RF-DC rectifier was  
Figure 3: Six-stage Dickson voltage multiplier circuit.  
connected to the proposed protection circuit, and two PMOSs (\(\rm{M_{1}-M_{2}}\)) and two NMOSs (\(\rm{M_{8}-M_{9}}\)) were diode-connected. Two bias voltages \(V_{A}\) and \(V_{B}\) could be expressed as follows:  
\[V_{A}=V_{dc}-\left(\left|V_{OD1}\right|+\left|V_{tp1}\right|\right)-\left(\left| V_{OD2}\right|+\left|V_{tp2}\right|\right), \tag{8}\]  
\[V_{B}=V_{OD9}+V_{tn9}, \tag{9}\]  
where \(V_{ODi}\), \(V_{tpi}\), and \(V_{tni}\) are the overdrive voltage of the \(i^{\rm th}\) MOSFET, threshold voltage of the \(i^{\rm th}\) PMOS, and threshold voltage of the \(i^{\rm th}\) NMOS. Under a common-mode operation, the two bias voltages were identical (i.e., \(V_{A}=V_{B}\)). The DC output voltage of the RF-DC rectifier can be expressed as follows:  
\[V_{dc}=\left(\left|V_{OD1}\right|+\left|V_{tp1}\right|\right)-\left(\left|V_{OD 2}\right|+\left|V_{tp2}\right|\right)+\left(V_{OD9}+V_{tn9}\right), \tag{10}\]  
Furthermore, the two bias voltages \(V_{A}\) and \(V_{B}\) could be derived from resistors (\(R_{1}-R_{2}\), \(R_{ds1}-R_{ds2}\), and \(R_{ds8}-R_{ds9}\)). Thus, the following can be derived:  
\[V_{A}=\frac{R_{1}}{R_{ds1}+R_{ds2}+R_{1}}\times V_{dc}, \tag{11}\]  
\[V_{B}=\frac{R_{ds9}}{R_{2}+R_{ds8}+R_{ds9}}\times V_{dc}, \tag{12}\]  
where \(R_{dsi}\) was the conduction impedance of the \(i^{\rm th}\) diode-connected MOSFET, which is expressed as \((g_{mi}+g_{mbi})^{-1}\) with the transistor transconductance \(g_{mi}\) and body effect transconductance \(g_{mbi}\). \(R_{1}\) and \(R_{2}\) are constant resistors. The larger the bias current \(I_{Ri}\) of the \(i^{\rm th}\) resistor is, the larger the transconductance \(g_{mi}\) is and the smaller the conduction resistor \(R_{dsi}\) is.  
If the output DC voltage \(\rm{V_{dc}}\) of the RF-DC rectifier was higher than the aforementioned voltage [Equation (11)], the bias voltage \(V_{A}\) was larger than the bias voltage \(V_{B}\) because of the reduced conduction impedance \(R_{dsi}\) with the large resistor current \(I_{Ri}\). The difference between \(V_{A}\) and \(V_{B}\) was amplified, and the differential output voltage \(\rm{V_{O}}\) was used to control the conduction current \(\rm{I_{O}}\) of the output transistor \(\rm{M_{O}}\). The larger the dc voltage \(\rm{V_{dc}}\) is, the larger the conduction current \(\rm{I_{O}}\) is. Thus, a stable DC output voltage ranged from 1.69 V to 1.76 V with an input power (\(P_{in}\)) ranging from \(-\)14 dBm to +10 dBm. Please note that the voltage variations of two biased voltages, \(V_{A}\) and \(V_{B}\), will be suppressed in the PVT (process, supply voltage, and temperature) variation. For example, if the resistor \(R_{1}\) is reduced with PVT variation, the bias current \(I_{R1}\) is enlarged. Then both conduction resistors, \(R_{ds1}\) and \(R_{ds2}\), are decreased by the large bias current \(I_{R1}\). As a result, three resistors, \(R_{ds1}\), \(R_{ds2}\) and \(R_{1}\), are reduced simultaneously to suppress the impact of PVT variation.