## 3 Simulated and Measured Results  
Figure 9 presents the simulated output voltage of the RF-DC rectifier by using a signal analyzer (EXA N9010A) at a distance of 10.0 cm between the antenna and rectifier. The operating frequency was 915 MHz, and the equivalent load was 1 M\(\Omega\). The simulation results revealed a minimum output voltage of 0.746 V at an input power \(P_{in}\) of \(-\)20 dBm, and a maximum output voltage of 21.693 V at \(P_{in}\) = +20 dBm. The proposed RF-energy-harvesting chip requires the over-voltage protection circuit to prevent the breakdown phenomenon, which is generated by high output voltages, particularly for NFC. Figure 10 shows the simulated DC output voltages of the RF-DC rectifier with over-voltage protection, which were limited from 1.773 V to 1.809 V with respect to the input power \(P_{in}\) from \(-\)13 dBm to +20 dBm. Figure 11 presents the simulated _PCE_ of the RF-DC rectifier with over-voltage protection, which is termed the rectifier _PCE_. It was approximately 43.601% at an input power of \(-\)7 dBm. _PCE_ is defined as that in [26]:  
\[PCE(\%)=\frac{P_{dc}}{P_{in}}\times 100\%=\frac{I_{dc}\times V_{dc}}{P_{in}} \times 100\% \tag{17}\]  
Figure 8: Complete circuit of charge control circuit. Figure 11: Simulated _PCE_ of the RF-DC rectifier with over-voltage protection (rectifier _PCE_), whose _PCE_ was approximately 43.6% at the input power of \(-7\) dBm. Figure 10: Simulated DC output voltages of the RF-DC rectifier with over-voltage protection. Figure 9: Simulated output voltage of the RF-DC rectifier with respect to the input power from \(-20\) dBm to \(+20\) dBm. The proposed LDO regulator provides a stable output voltage of 1.5 V and a load current of 30 \(\upmu\)A to the next stage-charge control circuit. When the input voltage varied from 1.7 V to 2.0 V and the reference voltage was 1.4 V, the LDO regulator performed with a quiescent current of 317 nA, and a maximum power efficiency of 84.835% was obtained at an input power \(P_{in}\) of \(-\)10 dBm. Figure 12 shows the simulated line regulation of the proposed LDO regulator. When the input voltage was varied from 1.7 V to 2.0 V, the output voltage changed from 1.5 V to 1.5108 V, and a line regulation of 36 mV/V was obtained. Figure 13 presents the simulated load regulation of the proposed LDO regulator. As the output current varied from 0.0 \(\upmu\)A to 10.0 \(\upmu\)A, the output voltage changed from 1.499952 V to 1.499968 V. A load regulation of 1.6 mV/mA was then obtained [27]. The charge control circuit was inputted with a pulse waveform, which is gradually ramped up from 1.2 V to 1.5 V, to charge the battery with the charging current of 16 \(\upmu\)A. When the battery voltage was charged to 1.4 V at 2.002 ms, the charging current decreased sharply, thereby reducing the charging speed. Finally, the voltage of the battery increased to 1.50 V with zero charging current. Figure 14 shows the simulated battery voltage and charging current of the charger control circuit. The maximum power efficiency of the charge control circuit was 84.835% at an input power \(P_{in}\) of +20 dBm. Figure 12: Simulated line regulation of the proposed LDO regulator. Figure 13: Simulated load regulation of the proposed LDO regulator. When all functional blocks were verified, the RF-energy-harvesting chip could be implemented using the standard TSMC 0.18 \(\upmu\)m 1P6M CMOS process. Figure 15 shows the layout of the proposed RF-energy-harvesting IC, which comprised the RF-DC rectifier, over-voltage protection circuit, CMOS voltage reference, LDO regulator, and charge control circuit.