# Parasitics Impact on the Performance of Rectifier Circuits in Sensing RF Energy Harvesting

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## Abstract

**:**

## 1. Introduction

## 2. Design Process

## 3. Choice of Components

## 4. Circuit Design

#### Optimal Source Impedance

## 5. Parasitic Elements

#### 5.1. Circuit Model

#### 5.2. Discussion

_{2}(molybdenum disulfide) [23,24], being applied to RF electronics. In particular, [24] presents a MoS

_{2}-based Schottky diode used as a rectifier in a RF energy harvesting system. To explain the different behavior of traditional Schottky diodes though, the junction and parasitic capacitances of this MoS

_{2}-based diode are in the order of 20 fF, 35 times less than those shown in Figure 10 and Figure 11. Since the parasitics of the diode are the most damaging, the performance of the rectifiers could be potentially improved with the development of MoS

_{2}diodes. Additionally, their cutoff frequency is also higher, which allows one to reduce losses at higher operating frequencies. As a comparison, the MoS

_{2}-based diode presented in [24] has a cutoff frequency of 10 GHz (zero external bias), while the HSMS 2822 diode utilized in this work only reaches up to 4 GHz.

#### 5.3. Final Circuits

#### 5.4. Performance Comparison of Passive Rectifiers

## 6. Conclusions

- The most harmful parasitics come from the components and not from the PCB. Therefore, if carefully chosen, cheaper PCBs can be utilized in order to reduce costs.
- Although the diode was known to be the limiting component in terms of losses, this work has demonstrated that it also causes a large deviation with respect to the expected frequency response. Actually, it has the most harmful parasitic element, contributing two-thirds of the total frequency displacements in both Cockcroft–Walton and half–wave circuits. In that sense, future MoS
_{2}diodes could potentially help to improve the efficiency of rectifier circuits, since their parasitics are shown to be very low [24] compared to traditional Schottky diodes. - The parasitic inductance associated with the capacitors is completely negligible. This fact allows one to use cheaper capacitors and reduce costs. It also allows one to use higher values of the capacitor in the rectifier stage, in order to reduce the DC output ripple when feeding the sensor. Note that the choice of this capacitor is a trade-off between the output ripple of the circuit, and its self-resonant frequency (SRF). The higher the value of the capacitor is, the lower the output ripple and the higher the parasitics. However, they do not affect the behavior of the circuit.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Example of a wireless sensor network (WSN) where the sensing devices are powered by radiofrequency (RF) energy harvesting systems.

**Figure 4.**Manufactured (

**a**) half-wave rectifiers and (

**b**) Cockcroft–Walton multipliers. The final half-wave rectifier was observed under the microscope. Label “Test” refers to the test CW multiplier and half-wave rectifier used to study the effect of the parasitic elements, and label “Final” refers to the redesigned final CW multiplier and half-wave rectifier.

**Figure 5.**Search of the optimal source impedance ${Z}_{s}$ in the Cockcroft–Walton multiplier and the half-wave rectifier.

**Figure 6.**Efficiency with respect to the source impedance ${Z}_{s}={R}_{s}+j{X}_{s}$ in the Cockcroft–Walton (CW) multiplier before (

**a**) and after (

**b**) considering the parasitics.

**Figure 7.**Efficiency with respect to the source impedance ${Z}_{S}={R}_{s}+j{X}_{s}$ in the half-wave rectifier before (

**a**) and after (

**b**) considering the parasitics.

**Figure 9.**Extraction of the parasitic elements from inductors and capacitors through their self-resonant frequencies (SRFs): (

**a**) measurement board and (

**b**) S-parameters. The SRF of an inductor is determined via the non-transmission peak in the $\left|{S}_{21}\right|.$ The SRF of a capacitor is determined via the non-reflection peak in the $\left|{S}_{11}\right|.$

**Figure 10.**Model for the parasitic elements in the test Cockcroft–Walton multiplier (

**a**) and their relevance in the efficiency of the circuit (

**b**). The values of the components are: ${L}_{v}=1.30\mathrm{nH},$ ${C}_{p1}=0.10\mathrm{pF},$ ${L}_{L1}=4.3\mathrm{nH},$ ${C}_{p2}=0.19\mathrm{pF},$ ${L}_{L2}=8.2\mathrm{nH},$ $C=33\mathrm{pF},$ ${L}_{p}=0.16\mathrm{nH},$ ${C}_{pd}=0.75\mathrm{pF},$ and ${R}_{L}=2.34\mathrm{k}\mathsf{\Omega}.$ The input power was ${P}_{in}=0$ dBm. Black and green dashed lines overlap.

**Figure 11.**Model for the parasitic elements in the test half–wave rectifier (

**a**) and their relevance in the efficiency of the circuit (

**b**). The values of the components are: ${L}_{v}^{\prime}=1.20\mathrm{nH},$ ${C}_{L}^{\prime}=2.7\mathrm{pF},$ ${L}_{p1}^{\prime}=0.38\mathrm{nH},{L}_{L}^{\prime}=47\mathrm{nH},$ ${C}_{p}^{\prime}=0.14\mathrm{pF},$ ${C}_{pd}=0.75\mathrm{pF},{C}^{\prime}=27\mathrm{pF},{L}_{p2}^{\prime}=0.04\mathrm{nH},\text{}\mathrm{and}\text{}{R}_{L}^{\prime}=8\mathrm{k}\mathsf{\Omega}.$ The input power was ${P}_{in}=0$ dBm. Black and green dashed lines overlap.

**Figure 12.**Monte Carlo analysis on the variability of the components in (

**a**) the Cockcroft–Walton multiplier and (

**b**) the half–wave rectifier. The nominal simulation and the measurements are also plotted.

**Figure 13.**Model for the parasitic elements in the final Cockcroft–Walton multiplier (

**a**) and their relevance in the efficiency of the circuit (

**b**). The values of the components are: ${L}_{v}=1.30\mathrm{nH},{C}_{p}=4.7\mathrm{pF},$ ${L}_{p1}=0.078\mathrm{nH},$ ${C}_{p1}=0.10\mathrm{pF},{L}_{L1}=4.3\mathrm{nH},$ ${C}_{p2}=0.19\mathrm{pF},$ ${L}_{L2}=8.2\mathrm{nH},$ $C=33\mathrm{pF},$ ${L}_{p}=0.16\mathrm{nH},$ ${C}_{pd}=0.75\mathrm{pF},$ and ${R}_{L}=2.34\mathrm{k}\mathsf{\Omega}.$ The input power was ${P}_{in}=0$ dBm.

**Figure 14.**Model for the parasitic elements in the final half-wave rectifier (

**a**) and their relevance in the efficiency of the circuit (

**b**). The values of the components are: ${L}_{v}^{\prime}=1\mathrm{nH},$ ${C}_{L}^{\prime}=4.7\mathrm{pF},$ ${L}_{p1}^{\prime}=0.078\mathrm{nH},{L}_{L}^{\prime}=27\mathrm{nH},$ ${C}_{p}^{\prime}=0.21\mathrm{pF},$ ${C}_{pd}=0.75\mathrm{pF},$ ${C}^{\prime}=27\mathrm{pF},{L}_{p2}^{\prime}=0.04\mathrm{nH},\text{}\mathrm{and}\text{}{R}_{L}^{\prime}=8\mathrm{k}\mathsf{\Omega}.$ The input power was ${P}_{in}=0$ dBm.

**Figure 15.**Monte Carlo analysis on the variability of the components in the final circuits: (

**a**) Cockcroft–Walton multiplier and (

**b**) half-wave rectifier. The nominal simulation and the measurements are also plotted.

**Figure 16.**Efficiency (measured at 870 MHz) as a function of the input power in the CW multiplier (blue) and the half-wave rectifier (red).

Model | Value | SRF (GHz) | Parasitic |
---|---|---|---|

4,841,372 (Fair-Rite) | 33 nH | 1.50 | 0.34 pF |

106–909 (Murata) | 8.2 nH | 4.00 | 0.19 pF |

795–8290 (TDK) | 4.3 nH | 7.64 | 0.10 pF |

464–6773 (AVX) | 33 pF | 2.20 | 0.16 nH |

532–2945 (TE Connect.) | 47 nH | 1.96 | 0.14 pF |

CW160,808 (Bourns) | 27 nH | 2.10 | 0.21 pF |

2,310,325 (Multicomp) | 2.7 pF | 4.97 | 0.38 nH |

ATC 500S (ATC) | 4.7 pF | 8.32 | 0.078nH |

2,809,454 (Kemet) | 27 pF | 4.84 | 0.040 nH |

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**MDPI and ACS Style**

Alex-Amor, A.; Moreno-Núñez, J.; Fernández-González, J.M.; Padilla, P.; Esteban, J.
Parasitics Impact on the Performance of Rectifier Circuits in Sensing RF Energy Harvesting. *Sensors* **2019**, *19*, 4939.
https://doi.org/10.3390/s19224939

**AMA Style**

Alex-Amor A, Moreno-Núñez J, Fernández-González JM, Padilla P, Esteban J.
Parasitics Impact on the Performance of Rectifier Circuits in Sensing RF Energy Harvesting. *Sensors*. 2019; 19(22):4939.
https://doi.org/10.3390/s19224939

**Chicago/Turabian Style**

Alex-Amor, Antonio, Javier Moreno-Núñez, José M. Fernández-González, Pablo Padilla, and Jaime Esteban.
2019. "Parasitics Impact on the Performance of Rectifier Circuits in Sensing RF Energy Harvesting" *Sensors* 19, no. 22: 4939.
https://doi.org/10.3390/s19224939